Answer:
Depends on what you mean by breathing problems, but no matter what you mean, it's potentially serious, so you'll have to take some action. Let's discuss options:
If you mean coughing or asthma that you're already aware of and is already being treated, continue the treatment your doctor recommended. When in doubt phone your doc or an ER to get more information. DON'T wait. And if you aren't sure, act.
If the child is choking, start on clearing that. Check the throat for obstructions. Heimlich maneuver is well accepted.
If your child isn't breathing at all, FIRST get someone calling 911, second start rescue breathing (the reason for this is that, no matter how good you are at rescue breathing, eventually you'll tire -- good to have some back-up coming).
If it's anything more serious consider a 911 call. Breathing problems can be very serious indeed.
Note that the faster you react, the better the outcome.