E.S.
I have had a sweat problem all my life. Never thought to talk to a doc about it and am extremely glad that clinical strength deoderant is on the market. I use Dove Clinical. You do have to put it on at night, but I have been known to forget it and be able to go two days and be fine!
I also have the big breast problem and have been known to use regular deoderant there (and the small of my back, top of butt crack, crease of legs-where thigh meets privates) I used to end up with sweat stains and water marks on the bottom third of my bra cups and have soaked underwear at the crotch and crack.
From some of the answers it sounds like Degree way even be better, but I like the sent of the Dove. If it ever stops working, I may try Degree.