Strange relatioonship between INTP and INTJ?

Hello.
Sorry for the long read ahead of time, but I want to give details, so you could comment knowing all the information and wouldn't need to ask many questions afterward.
My personality is INTP, and 7 months ago, I've met a girl whose personality type is INFJ. I am 20, and she is 16. We spend most of the time chatting on MSN, and we only have met 5 times during this period of time. Currently she has been to Poland with her parents for a week, and so we haven't had any contact, because she didn't have the internet here, and we don't use our phones much. During that period of time, my computer has broken and I do not have money to repair it, so I am using a computer with another OS and I cannot install nor use MSN. I've send her an email, and I'm sure that she received it. (she checks her email every day) The only thing that would keep us in contact is phone, and neither of us have send a message to each other for a week after she got back.
I am wondering if I should take a step and write her a message or not, because of the following details:
She never asked me to meet her. What happened is I always unconsciously asked her to meet me, and just noticed it afterwards (talking about going out, etc..), then she would ask me out. We are both very shy... I noticed this behavior, because my family is poor, and I'm not in a very good situation, she knows all that, and I think that she might feel sorry for me and that's why she would meet me. Not only sorry for me, but she might not want to hurt me, because she knows that she is the only friend I've got. I am very open with her, so she is with me. According to her personality, she should hate criticism, but she asks me to tell her the truth, and I like that, I hate lies. However, sometimes it is criticism, but it seems that she is okay with it, and I am good with body language...
So when I'm meeting her that way, by asking her to ask me out unconsciously, I feel like I would be using her. I don't like that feeling, I even hate it. However, I enjoy meeting her, being with her, talking... So I don't really know, if I should ask her out, or just keep it the way it is and wait and see if she will ask me out completely by herself. If I will ask her out, I will again feel like using her and I will feel bad, and it will all start over again, but if I will not ask her out, I am afraid, that the relationship will end...
The thing is that she is thinking that she is a person that nobody wants to be with, she thinks that she is uninteresting, so she might just think that I want to not be friends with her... However, when she talks about her relationship with others and thoughts about the world, I tell her that I like being with her, and I want to be friends, so she knows that... She cannot think that we are friends because I need something from her, because she doesn't give anything, except friendship, nor do I. We just go and sit somewhere and talk for 4 or 5 hours, during all these 5 meetings we never went to a restaurant or something like that.
Another thing that makes me think that she just doesn't want to hurt me and she doesn't want to be friends is that she is going out with her friends every day, and every day, she says that she doesn't like doing that: it is not interesting to her. But she still does it.
And the most concerning thing is that when she offers to meet, she always seems like she wouldn't want to do it, seems like she'd say that she doesn't care, but when I mention it, she says that she does want to meet me, even though it feels like she wouldn't. It also seems that she has a great time when meeting me, but before meeting me - she seems not wanting to do it.
Another reason I think that she doesn't want to be friends with me is that she doesn't have anything to do during the evenings, she chats with people or watches videos on youtube, or plays some browser-game, like travian, etc, so I think that I might be just something to occupy her during the time she does nothing... But the fact that she tells me a lot about her inner self doesn't make sense then though...
Some interesting facts: she wants to be a guide in the future, (moving trough countries, telling the tourists about the country, showing places) or a photographer. (again - traveling, not staying in one place) When I asked her why, she's told me that she doesn't want to have a relationship with anybody, because people can hurt you. And traveling would prevent her from having a relationship. She seems to be running from deeper relationships, but she is very open with me, she tells me almost everything about her feelings, emotions and her thoughts. (haven't told me only a few things, and 3/5 of them are about me) I am the only person who she talks to and tells that everything... She is the only person I tell that too.
I think that I might've gotten too close to her, and she is now running from it, because she doesn't want to have the relationship, because of her beliefs... (even though it's obvious that I'm not going to hurt her) I don't know if I should chase her or not. I don't know what the outcome might be out of this.
She seems to be hurt 'in the core', even though nobody hurt her, she never had a boyfriend, while I never had a girlfriend. (we didn't have close friends too...) She seems to think that she is worthless and shouldn't be in a relationship... I can't even tell if she wants it, it seems like she is hiding all her wishes and everything that she might want, or that might hurt her in some way, in a shell, and she is hiding from them and lying to herself, that she doesn't want anything closer than a distant friend who knows only what movies she likes. I know the feeling of hiding too, but this time, I stepped out of the shell.



Sorry again for the long read, I hope it wasn't boring. :/

So here is the dilemma: should I call her and ask her out and feel bad about it (feel like using her), and hope for something that would stop make me feel like that... Or should I leave it and wait for her to call? (if she calls, if not - the relationship has ended, I guess... It's been a week already)
I don't want you to give me a direct answer to this, I want your thoughts about what could be going in in an INFJ's head, what could be the possible reasons and outcomes and all that.

Thank you!

 

Yes, I do... However, my personality makes me to over-think things. Even though I want her as a friend, I want her to want the same. I don't want to 'use' her, in other words - make her to be friends with me because of my 'situation'.
And I am not sure if she wants that and is running from it, or she doesn't want that and is just trying to make me feel better.

 

I don't really care which one, however I don't even know the main differences between these two, except 'romantic' things, like sex or whatever...
Maybe the girlfriend concept would be something new, like a new discovery or something. But I'm fully okay with being her friend, without the 'girlfriend' part.

 

I did, she says that she wants to be friends, but it's logical that one human being doesn't want to hurt another by telling him the opposite... And adding my situation...
Basically I'm just looking at two possibilities: she wants to be friends and is running from it, or she doesn't want to be friends, but doesn't let it go, because she doesn't want to hurt me and feels sorry for me.
I believe her, when she says that she does, but at times it seems that she doesn't...

That's why I posted a message here - so other INFJs could possibly talk from their experience and point me to the right direction, help me explain how she really feels, etc..

 

Okay, if I have to choose... I want my relationship to be friends, but if she will want to sometime - I won't mind changing it into the girl/boyfriend...

 

And that is why I want to be only friends with her...

 

Unfortunately, that doesn't help me to fight my loneliness, acd. I need somebody that I could talk to, and somebody that would feel good to talk to.