Sick 1 year old, so stressed out!

✩M

My son will be one next Wednesday. He woke up with a fever Wednesday morning of 102. I gave him some Tylenol, and waited to see if it would help, it only brought it down one degree. He took a nap and when he woke up, he was visibly sick. Flushed cheeks, acting lethargic and I quickly put him in the car to take him to the doctor. When we got there he was 104! The doctor took his sweet time coming in to check him. He looked in his ears and throat and checked his lymph nodes and announced he had no other physical symptoms and no "reason" for a fever. He said it was probably just a bug and had him given an antibiotic shot and ibuprofen. He never swabbed him or did labs. Didn't check for a UTI. He sent us home with a prescription for an antibiotic and said to call if the fever didn't go down. But if he doesn't know what's wrong with him or thinks it's just a flu bug, why did he do that? If he has the flu, an antibiotic isn't going to do anything. I'm really frustrated. The fever hasn't come back since then, but he's been up late every night crying and screaming (he's teething, but he wasn't doing that before he got sick.) The antibiotics gave him a rash and he's had diarrhea twice today. Apparently those are normal side effects. I just don't know what to do. I'm so scared something is really wrong with him and I don't know about it. I feel like his doctor hasn't handled any of this well. Would this make you upset? Am I overreacting? Outside of the crying at night, he's more or less avting normal. He's not eating much, but I think his mouth hurts and his stomach is upset from the medication. Someone please tell me my son is just sick and teething and that he'll be okay, I'm so nervous and his doctor doesn't seem concerned at all.