Antibiotics have nothing to do with viruses. Your child likely is picking up viruses separately from the infections for which he's prescribed the antibiotics.
The symptoms you describe sound like typical stomach virus and are not a reason for going to the hospital. You expose him to more germs and viruses when you take him there. Do you call your pediatrician before you go? Is the pediatrician advising you to go to the ER? I would bet not -- please call the pediatrician first next time. If your pediatrician does not have a system where you can call 24/7 and get a real person to call back to answer your questions about whether a hospital trip is needed -- you need to change doctors to one who does have such a system. Most do.
It is possible that he is weaker and more susceptible to viruses after he's been sick with an ear infection but the antibiotics themselves are not going to "cause" a viral infection.
Is he in day care or preschool or kindergarten? Do you send him back to any of those once he's had a few days of antibiotics? (It's typical to return to school etc. after 48 hours on most antibiotics.) If so, then he is likely picking up viruses at school, unrelated to his ear infection or the medication.
I would work on getting his recurring ear infections handled better (he may need an operation on his tubes). And talk to your doctor before the next time -- tell the doctor about the hospital visits. You are leaping to the hospital very quickly and possibly exposing him to more infections when there.