L.R.
Hasn't your doctor done any cultures on your son's throat etc. to see if this is bacterial? If he has, and it it is bacterial, then antibiotics can help; however, if this is viral -- and it sounds like it might be, or even an allergy (yes, they can cause just those symptoms), then antibiotics will do nothing and you will continue to be frustrated.
There are virulent colds going on around here where kids, and adults, have these same symptoms for three weeks, a month, even six weeks. A cold won't be affected by an antibiotic and neither will a viral infection. Allergies certainly won't. It's hard to see a child as young as yours going through this, but getting the wrong treatment won't help him, or ease your frustrations.
I know it's not what you want to hear but -- these symptoms going on for a month does not translate immediately into something for which your son needs antibiotics. I'm kind of surprised the doctor agreed to give them if he or she was sure this is viral.
I would go to the doctor; say you were very frustrated, and ask if there is a test that can help you understand if this is viral or bacterial. Then go from there regarding treatment. If antibiotics are appropriate, great, but if they are not, please don't insist on them just to feel that the doctor is "doing something."