Boobs and bras (sorry--it's long!)

Okayy. So I'm going to start off by saying this is very awkward for me to write, but I don't know where else to ask and I know the people here are kind. So, by the title, you can probably tell this is about boobs. I'm 12 years old, turning 13 on May 2nd. I want to know how much they'll develop over the years. Mine are in stage 3, I think. I started puberty in 4th-5th grade and I'm in 7th now. My first period was last September. I currently wear a 34B, but I'm pretty sure it's the wrong size. So, do they just grow all at once, or do they just slowly get bigger? I started wearing a bra in.. 4th grade I think? A training one, but still a bra. I wore padded ones in 5th or 6th and now I wear underwire. It's really uncomfortable for me because when I'm running or jumping (especially in class) and they bounce all around and it hurts. My mom refuses to buy me bras and it's very frustrating. I had a lot of trouble with non-underwire ones and I told my mom that I wanted to try underwire because they were hurting me and she didn't believe me. She told me I just wanted an excuse to go shopping and that underwire was just a pain and I don't need it. After a few days I got upset and texted her exactly what was going on. She got me 2 bras from target and those are the only ones I have. The straps are constantly falling down, there are sometimes a few small gaps in the bra.. And the underwire kind of sticks out. Like, it's not Coming out of the bra, it's just not laying flat so I can't wear tighter shirts, of dresses. Before when we were at a store I randomly tried on a bra to see if it fit and she randomly came in and I told her it didn't fit. So she said she'd take me to get fitted. I asked her a few days later and she said I didn't need it and I'd survive. -.-  whenever I ask for anything I need she thinks it's and excuse to go shopping and it's really frustrating. So.. I can't really get a good bra so I just have to bounce everywhere I guess. Will my boobs just randomly have a growth spurt or just grow slowly? I've been growing a lot in the past year and a half, I've probably grown 3 inches in 2 months. I know because before einter break I was shorter than my dad and after I was the same, and now I'm taller by an inch and a half-ish. My pubic hair is in stage 3/4ish. I know this might be tmi, heh, but I'm just looking for information.. I can't find anything online. So, uh.. Yeah. Thanks for answering my questions and sticking around this long, haha. Sorry it's so long. Thank you!