That's pretty unusual, at least in my opinion. I'm a 32DDD/F (different from when I first posted this, I lost weight) and I usually only get backaches from wearing a poorly fitting bra. Now if I go braless, I usually don't experience any problems like what you're describing. Then again, I go braless practically all the time (since I used to wear such poor fitting bras) so maybe I've just gotten used to it.
If you don't mind me saying, you may want to be remeasured (just for size confirmation) and fitted with some good bras. I recommend Warner bras, which I can't wear anymore since they don't come in a band size smaller than 34. But still, they have some really comfortable bras.
And instead of going braless, you might could try a loose fitting sports bra.
I know you didn't ask for it, but just in case you want some tips to ease your pain, there you go. Oh also, if you don't know how to properly measure yourself, I can tell you. I had been doing it wrong for years until I saw this video one day. I had been in a 34D only to find out I was a 32DDD/F! It was quite a shock. But basically your boob fat can settle on your sides and your back, so you have to lean over to measure your full bust. In case you didn't know that, that is. Idk, I'm just mentioning it since most women wear the wrong size and thus experience a lot of discomfort.