help needed with weightloss...

Unfortunately, you'll have to just reduce overall body fat. No matter how many back exercises you do, you can't target this one area alone. You'll probably just end up building muscle here if you go at it long enough and that won't help your problem.
Even just a few pounds of body fat lost can make a huge difference...if it fits everywhere else, seems like you don't have a lot to lose. Try heavy cardio (running is the best I think) for a few weeks, going every day or every other day. And watch your diet! Cut out the crap.

Have you tried a different bra? It's not fitting at that area because its not large enough around your chest. Try a non-padded one that fits tightly?? Might help.

i'd try different bra, spanx, etc , but other than that all you can do it try its hard to guess how much you'd have to lose to fit the dress to many factors involved for us to guess or estimate if you could lose it by prom.