With the measurements you've given, you are about a 42AA. They don't make bras that size.
[Edit: Amoena does.]
I've seen ones like eBay item #303508353573 which come in up to 46AAA, but I don't have any experience with them. [Edit: There's something very wrong with their sizing. They seemed large, so I tried an AA, and what came was at least a B; so I ordered again, a AAA this time, and what came was at least a C, my wife's size.]
You could try some XXL or XXXL compression/sports bras. Many people find them uncomfortable.
I started having severe nipple fissures from the buzzing of my snug jerseys' tiny wrinkles in the wind while riding bike even before I realized that breast was growing. That was three years ago. I tried the NipEAZE nipple stickers, but they only worked initially, remedying the fissure problem; but after some growth, I needed more help to avoid soreness and irritation even when not riding bike.
I found that a few male marathon runners were recommending a sports bra, and I finally gave in and first got the Fruit of the Loom type 9012 cheap pull-over sports bras that are very, very plain. Wow, what a relief, and to more than just the nipple! My underbust is 37", and I do best with their size 40. Still, they, like a few others I've tried, kind of bite into the lower fronts of my shoulders a bit. I tried their 9036 with the thin straps, which was better in that respect and therefore more comfortable, but they're a little harder to hide. (They come in packs of three; and as far as colors go, the gray seems to hide the best. They don't have skin color.) I also tried a few other types, including some super cheap ones from China that worked well, in size L or XL. Some L's I've gotten were too small, and some XL's were too large, as the manufacturers don't all work to the same size standards. Except on the bike, I mostly wear the Jockey Air Seamfree for its comfort and that I can hide it well.
These are all bralettes though, and basically smash my breast down; and although they prevent friction on the inside of my shirts and hold it in place better, I think it would be more comfortable if I could find a bra that has an actual cup, or at least gives my breast some room without being so loose everywhere else that the rest moves around. I have a few more types coming. Hanes has been having big discounts recently, so I have a couple coming from them this week.
The problem with ordering really cheap ones from China on eBay is that it takes so long for them to arrive, that you decide "This one's perfect [or will be in the next size up or down] so I'll get three more," and by that time the same one is not available anymore, so you have to start over. It's a bit frustrating. I have not gotten my nerve up to make an appointment with a lingerie shop and get fitted. Besides the obvious, I suspect they wouldn't have anything in my size, so it would be a waste of everyone's time.
I tried posting a couple of pictures with this, but it wouldn't post. I tried several times, even after having removed the pictures, and the "Post" button just gave a tiny window that said "Ok" but otherwise did nothing. What's the secret? I will
not put them on my website to link to! Now I've logged out and back in and we'll see if I can get just the text to post.