Thank you so much for your question. It is my privilege to be able to help you.
It sounds like your going through quite a bit these last few months! And you're getting a hysterectomy soon! I hope that everything works out for you and you can get back to normal life after you recover from all of your treatments and surgeries.
As far as the odor and the brownish discharge, the most likely cause is Bacterial Vaginosis
(BV). BV is caused by an overgrowth of certain types of bacteria that are native to the vagina. Things that change the vaginal environment can cause it, and if you had antibiotics or other medications during the surgery that you had, that may have been the cause.
At first when you mentioned that it happened right after your period, I thought that it must be just old blood from your period, but when you said that it happened a few days later again after sex, I think it is probably BV.
Your doctor can treat it with antibiotics, either by mouth or a vaginal gel. Both metronidazole and clindamycin can work.
It is also possible that it is a sexually transmitted infection, if you think that may be possible. Your doctor can do cultures to rule this out. However, I think that BV is most likely.
I don’t know what to tell you about the burp that you described, but it sounds like reflux. This can also get worse when your body has just been stressed by a surgery. You should try Tums or Maalox, and if it doesn’t get better with that, speak to your doctor about possibly getting a prescription for it.
I hope you find this helpful. If you have any more questions please feel free to ask me. If you are satisfied, please remember to ACCEPT the answer so that I get credit for my work. BONUSES and positive feedback are always appreciated. Good Luck! Dr. SaulJE