Yikes
I've seen and experienced things that
seemed or rather
felt emotionally traumatic at the time, but no PTSD.
The problem with getting PTSD because of your parents is that they should be the people teaching and helping you through trauma. When they're the ones who cause it, you're pretty much screwed unless you have better mentors around.
Also, it seems to me that your siblings narcissistic tendencies could be their coping mechanism for what they went through. Whereas your response may be PTSD. Bad situations naturally bring about negative coping mechanisms.
People respond differently to situations. I don't think this is really a type thing since people's personalities go beyond their mbti. Even If there is some type/PTSD correlation It would be difficult to prove.
My suggestion to you is to consult a professional. We are all overly biased when it comes to self-diagnosis. If you'd prefer not to talk to a professional, perhaps a close and trusted friend (not for diagnosis or even advice, but for the automatic therapy that comes from confiding in someone who cares about you.)