You definitely want to get him in to an allergist. HIves don't progress to anaphylactic shock, they are considered to be part of an anaphylactic response, as is vomiting, even without the breathing problems. The breathing problems can come anytime the hives are on the face, or without hives. When I learned that I was pretty scared, because I had only been giving Benadryl for the hives if they bothered my son.
The reason I say an allergist, is that many doctors who have some training in allergies don't have enough information to give completely accurate help. We went to National Jewish Hospital when my son was 3.5 and learned everything we "knew" about my son's allergies was wrong. That's when I learned the about about hives.
Even though your son is so young, a skin test should still be done and then blood tests if the skin tests indicate a need. In reality, neither is really accurate until around age 3, but the information we've gotten has been helpful for our two younger ones.
Once you get it figured out, it's really not as scary as it may seem right now. One thing you can do in the meantime is start a diary. Include everything he eats, at what time, and how much. Mark down anytime there is a change in weather or environment, say a trip to the park, etc., as well as anytime you change any cleaner in the house. Of course, you want to keep track of when hives started, where they were located, how you treated them, and how long they lasted. That information will get you light years ahead at your first appointment. Who knows, maybe seeing it all in writing, you'll figure out the culprit. Good luck!
P.S. Sometimes kids just have random hives. My son, as well as one of his friends both get them for no known reason. In that case, there is no need for alarm.