Wow, your progress is looking very nice! Seems you've got yourself a good routine going on for yourself.
As for the Bra, if they are bouncing around a lot, then yes, I would say finding an appropriate bra would help keep them from chafing. Trust me, you don't want to get raw nipples, it is NOT fun.
I actually don't wear a bra because of the type of polo t's I wear, it would be VERY obvious I was wearing a bra. What I have found that works best for me, are form fitting camisoles. Not super tight, they could almost, maybe maybe not, be taken for tanks. If it weren't for the cut, and colors, oh the lovely colors. Sorry, anyways, the form fitting camisoles acts as a barrier between my chest and polo, shirt, t-shirt etc. So I don't get the bad rubs anymore.
Thanks for sharing your latest progress!