I completely agree with Tija, and I know exactly how you feel! My son (22 months) has always been the the kind of kid we could take anywhere, and he'd be an angel. We'd get strangers telling us how well-behaved he is. He was the kid that the other parents wished they had!
That ended about a month and a half ago, and we can't take him to restaurants, because he won't eat or sit and throws fits. He often runs from us in stores, won't sit in the cart, and screams at diaper changes and when his teeth are brushed. He was so terrible at a weekend visit to see family they almost asked that we not bring him back! (Not really, but the thought probably crossed their minds!) But we realized he only acts like this now when he's getting teeth. The canines have been worse than the molars. And goodness I hope those teeth come in soon! His teeth have always taken forever, so it's agony for all three of us!
Just keep doing what you're doing. Stick to your guns and don't give in to the tantrums. It IS difficult to do at a restaurant - I also feel that taking him out just supports the behavior, because he needs to learn to sit in his chair and eat, and taking him out just gives him what he wants. But I hate to disturb everyone else, so we take turns taking him out, but when we do, we don't let him down (because he wants to run around). We hold onto him and let him throw his fit, and it gives the message that he's not going to get what he wants, no matter what. It's exhausting, sure, but I'd rather do that than give in to him. We also don't want to become those parents who don't ever go to restaurants because they're afraid of how the kids will behave! Nowadays we choose to go to smaller, less "busy" (as in decor) places, and at off-peak times. The fewer the people, the better. He's a sociable kid and he wants to see everything and everyone, so the less that's going on there, the better. We also noticed he behaves better at the places we frequent, and earlier in the day. Going out to breakfast seems to be okay (so far).
I first started giving my son clothing and food choices several months ago, and he didn't get it at first, so I just pretended he chose something. But now he does decide half the time, and the other half, he just doesn't care. It's a simple thing, but I think he enjoys the fact that I'm giving him the choice, more than he truly cares what shirt he wears that day.
Again, stick to it and don't give in, because while it seems easier, it really causes more problems in the long run. Good luck, I hope he (and you!) gets through this phase soon, which I hope for my boy as well!