If you have a PCP you can talk to, share your problems taking antibiotics (I have that problem as well, and get gastritis whenever I take it). The ones I can tolerate are Amoxicillin and Z-pac, although the last time I took a Z-pac my stomach reacted more than I expected.
There is one other back-up antibiotic choice, and that's Rocephen. Rocephen is injectable, so you'll bypass your stomach. I've only had it once--when I had a lung infection before, during, and after my Nissen surgery. My PCP understood my stomach problems, and went the Rocephen route to avoid irritating my healing stomach.
Good luck finding something that works for you.