I pick up things in a very physical fashion, also. I pick up random people's aches and sometimes searing pains. If it's really bad I might involuntarily exclaim - one woman looked at me oddly andsaid, I've got a pain in that area since giving birth... Those sorts of pains leave once I leave the company, or a short time later. (Headaches may linger.)
I also get the burping with certain foreign energies. If I burp, myself, it's for a reason. This other sort of burping is compulsive and ongoing and attached to nothing currently going on in my digestive system. It's very particular. In "The Shaman in Stilettoes", the Peruvian shaman teaches the author that energy is released via the mouth or anus. I can vouch for that, with these sorts of pickups! Which doesn't mean all gas is foreign energy. I get the burping mostly with distance energy, soI don't have so much public embarrassment; or I'll find I'm burping after a trip to the supermarket. I get a lot of interesting headaches in group settings, also.
It all sounds of course very wacky. I think we have to learn to discern over time what is ours and what is not and how to deal with it. I do find a meditation helpful to seive things through and also calm the body, and I keep records of occurences (lots of WTF!) to help glean whether or not I am picking stuff up, likely sources (I do generally know who, and certain pickups have unique 'signatures' to them). It is all very tiring.
Most empaths seem to be more emotional, mental. My 'gift' is very physical. Sounds like yours might be, also. Best advice I can give is the old adage, 'Know thyself.' And give it time. It's a trip!