I know with GERD you aren't supposed to wear tight fitting clothing, especially like tight jeans or tight shirts. maybe a sports bra would help? I'm sorry I've never heard of a support vest, it is similar to a sports bra? some shirts do have built in bras, but I am not sure how effective it will be for you.
Just to let you know, I don't know if you know this or not, but I heard to drink water 30 mins BEFORE and 30 mins AFTER eating will help, instead of eating and drinking water at the same time. Maybe this will help decrease the heartburn. I've been eating more apples recently and that has made me have less heartburn, maybe it will work for you too?
If I find out the answer to your question, I'll let you know, but I am not sure, but maybe if you visit your doctor, he/she can you the answers and maybe can give you advice
Good luck, I hope you heal quickly!