Should I start wearing a padded bra?

I'm 15 turning 16 this December 2012 and I haven't worn padded bras yet. Like the ones in Victoria Secrets. I went to Victoria's Secrets and got my size and I was a 32B. Yes I still wear training bras...well thick cotton bras that teenagers in Vietnam used to wear when they were around my age. My mom wouldn't let me wear a real bra because she said they will make my shrink cause of the wire and the mushy thing. Do you think I should? And will it shrink my ies, cause I think they're pretty itty bitty. D':