Why did my puppy just vomit? Should I feed him?

if he's acting normal, then I would imagine he vomited because of all the treats. Treats are supposed to be just that, treats; let's just say it's the equivalent to you eating chips and chocolate bars all day long with no actual food, I'm sure your tummy would be upset too. Try feeding him a bland diet (for his tummy trouble), like boiled chicken and rice, then tomorrow give him his normal food (though don't push the rations)