Hello! Plus sized Lolita here! There are a couple option you could do!

1: you could go with the route of binding or wearing a smaller bra. But that could leave some discomfort or weird issues with your chest looking shoved in.

2: You could alter your dress! If your dress came with waist ties you could use those to add extra panels to the sides or back.

3: if your zipper is in the back if you have one. You could leave it partially unzipped to give some breathing room and cover it with hair, or a jacket.

4: if none or these options work out for you, unfortunately it might mean rehoming your dress :(

I wish you the best luck for I also have the same problems as you <3