I have no advice.. so sorry you are going through this! But antibiotics do not bring fever down. Did the dr tell you to stop fever reducers ( Tylenol, Advil etc). Hydration is a must! Maybe getting smart water ( it has electro lights without the unnecessary sugar like Gatorade)
I say call his dr and ask.
Also antibiotics ruin adults stomach lining ( flora) .. i can imagine what they can do to a kids! I suggest to eat yogurt I think 2 hours after a dose of antibiotics.
I suggest when your child gets better to be super strict with hand washing as soon as you guys come home. I also have a hand sanitizer in the car ( but hand washing when walking in is a must). And this one surprised me.. about a year or two after my kids started sports ( oldest was a little after 4 we had them in sports. Their immune system was soo weak.. it seemed every week they would get something! But I kid you not it has been years and years since they took antibiotics or any medication.
I hope he feels better and soon! And try not to stress!