The short answer is yes, cat antibiotics can have side effects. The most common side effect is vomiting, which can occur with any antibiotic but is more common with certain types. Other possible side effects include diarrhea, stomach upset, and allergic reactions. These are usually not serious and go away once the antibiotic is stopped. However, if your cat experiences any of these side effects, or if they seem to be getting worse, you should call your veterinarian.