1 year old with swollen gums

We took my one year old to his pediatrician almost two weeks ago. He initially was up most of the night with a dry cough. They said he had an irritated throat, ear drums were swollen, and some congestion.  They started him on amoxicillin twice a day. The following day he was wheezing very badly so we took him back.  They diagnosed him with inflammation in his lungs, gave a shot of steroids,  along with a liquid form to continue over the next few days. We also started him on breathing treatments with Albuterol through a nebulizer.  Fast forward to three days ago, he started a low grade fever and while drinking from a bottle you could tell his gums were sore. We just thought he was teething again, and didn’t think much of it. We had reduced his breathing treatments to three a day, and yesterday he had his last one. After being awake much of the night last night, we wake up to discover he has a sore on his lip, and latter after forcing him to let us look in his mouth, we notice his gums are so swollen that his 4 top teeth are barely visible. A trip to the ER brings a diagnosis of hand foot and mouth, and swolled eardrums. This after 10 days of amoxicillin.  After researching the net I find nowhere listing gums swelling to this magnitude as a symptom.  Is this possible? I understand that if it was an allergic reaction to the Albuterol it should have manifested within the first days of treatment. Or could it happen after multiple treatments?