There is plenty of drinking to be done that's not shots. Shots make a lot of people feel gross. I would stick to beer, wine, and mixed drinks.
Are you sure you don't have some kind of alcohol intolerance? Are you on any medications? Not to be a bummer, but my suggestion would be to not drink, at least until you determine what the cause is. Or if you can tolerate one beer, but not two, just have one. Some nicer bars have beer samplers so you could have a few really small beers and get to have multiple drinks but not have to barf later.