Afraid to ask for Bras

I am quite young and have what I believe to be larger breaths than most kids my age (13). I kind of had a fear of puberty growing up. So I REFUSED bras until like 10 so started in a A cup and that’s just what fit me best. I wore Walmart bras until they started to hurt and my boobs would spill out around like early 12 or so so then my mom gave me some of her old ones because we didn’t have much money. So they fit nice and I went straight to a 34 C and they were really comfortable. My grandma (who had just gotten a bonus) decided to take me out to get some really nice bras at PINK. Then she moved. And since she got me those I have progressively started to not fit into them. Until now my boobs are spilling out and there’re the only bras I’ve had and again we don’t have much money so I don’t want to ask for new ones in a bugger cup size because I know my mom will really try to get me nice ones. And oddly enough I’m kind of scared. Like I don’t want to tell her I need a D cup. It almost feels like I’m lying. And I don’t know why. I think it’s because my mom wears that size and she has bigger boobs than I do, and I don’t want her to think I’m lying. When I told kids I wore a C they called me liars and said at best I could fit into their B cups, which I’ve worn and find uncomfortable. But maybe that’s just because I’m used to a bigger cup size than necessary...? I dunno, this probably makes no sense I just wanted to rant.