I would immediately seek a 2nd opinion from a different doctor. It may be allergies, or maybe not. The mucus especially if it has color to it, would concern me.
But why take the chance?
They have given him some high powered drugs and they haven't done much, I would NOT continue to do so, unless told to by a different doctor, as giving a small child too many antibiotics at an early age can actually make his immune system unresponsive to antibiotics later. Just be sure you follow the instructions exactly though, you cant give it to him for 2 days and he feels better and you skip a day, etc. (I'm not suggesting that you've done anything wrong, just an FYI to the public)
Seek a 2nd opinion, if your doctor does not seem that concerned about this, find another doctor. After a month and 3 different drugs and several visits to the doctor, if my kid hadn't improved, and my doctor wasn't as concerned about this as I am, I'd be looking for another doctor.