Hello,
Well a big chest means quite a bit of weight pulling you down and front. Deppends the size we talking about. From the few i can understand sounds like the back shoulder muscles are weak or require more strength training in order to withstand that weigth pulling in the front.
As humans we tend to do pushing exercises in our daily lives eg push ups or work base rounded shoulders while on the pc or office doing work. Causing what we call Upper cross syndrome that is muscular weakness and tightness at the same time
So you have the options to visit a physio or a proper personal trainer to advise and prescribe you Scapula and pulling exercises eg rowing or reverse flys.
Do you also get low back pain when standing or at prolonged sitting.
Please consider that you may get quite a bit of definition at your hands and shoulders in order to get things balanced. If you like to keep a feminin appearance and not muscular then reduction may be a good solution avoiding other side effect in the future.
I hope that helped a bit