I'm 15, 129lbs and 5'6 with a 32g bra size. It really affects my posture. Could I have reduction?

There is the possibility that if a doctor thinks it might have a long term effect on your health (and it sounds as though it does), they might give you a breast reduction when you turn 16, this is reliant on the doctor being keen to do it then, some might want to wait until you are 18, which is ridiculous, they aren't going away by themselves!
Visit your GP and ask him to refer you, don't take no for an answer, he will then arrange for an appointment with a specialist, if you go now you might not have to wait as long, waiting lists are long but if they aren't going to operate until you are 16 you could do the waiting now.
Good luck!