I'm a teen who has the same reoccuring problem. I meet a girl who is very seeet,funny,smart,charming,etc but it always turna out she's been hurt or injured or damaged some how by someone and I want to rescue her. Be her hero. Is this normal or doni have a white knight complex?

Well, I say I did. I just realised that I met my ex when she had a broken ankle and was on crutches. And I have a long running daydream of dating someone who uses a wheelchair.
Ack! Self-realisation stings!
I suppose the question is: would you be attracted to someone if, with your help, she completely recovered and became a confident, outgoing, happy person? Or is there some part of you that would prefer her to stay damaged so that you're always there to pick up the pieces?
I'm not criticising, by the way, but there are plenty of women who would be wary.
You pretty much said this in your original post, though and so I do believe your motives are good. It takes patience, tolerance, and care to be there for someone with problems. And I think these are pretty good attributes to have. I hope you'll get your chance to make someone's life better. It's a win-win situation. Good luck to you!
Needless to say, the relationship I'm in now has showed me that it's a bad foundation for a relationship.. Haha.