I'm not sure what to make of this

When you say it's rather clear, does she seem to acknowledge you more than anyone else in those situations? If the attention she is giving is unique to you, then the next time she smiles and says hello, you could say hi, and then ask something trivial to start a conversation, just to see how she responds. I suggest that doing that rather than going up to her and initiating something on the spot. Best of luck.

 

You should try to talk to her. Don't afraid or get scared of anything. may be that girl wanted to take care of yourself.

 

Is she making eye contact with just you? I know you said your not sure, but sometimes our perception is skewed by our self esteem. If she made eye contact, the hello was a deliberate attempt to reach out to someone she finds interesting. Take it slow, say hello back next time. After that introduce yourself.

 

I hate when this happens 9/10, the person knows me from a year or two back and I don't even remember them. Sometimes I get lucky and someone will introduce who they are either because that is their personality or they caught on to the fact that I didn't know who they were. Sometimes I have to bluntly say "I don't know who you are."

I know this isn't your situation at all but it just reminded me of when this happens to me.

 

what I mean by take it slow is say hello first, introduce yourself next (if given the opportunity), then let the pieces fall where they may.

 

First off, did she look you directly in the eyes when she was saying hello? Even though she was walking was her body language open to you? (Did she look at you from a distance, or only up close)

Somebody saying hello is a sign that they wish to talk to you. The only time I could hear it otherwise would be if she was trying to get something out of you; perhaps she would like help in one of the classes you have together.

It's hard to figure out why people do things, the easiest way would be to ask her!