I definitely agree about allergy testing. Allergies can certainly cause the repeated symptoms he is having. Another issue culd be GERD, so evaluation for that might be a good idea.
As gemingirl1963 said, repeated use on antibiotics is not good. The bacteria become resistant and super bugs like MRSA are the results. One of my daughters had repeated ear infections. She was put on a maintenance antibiotic for a while (I think one of the ones used to treat acne). In addition to bacteria becoming resistent to the antibiotics, repeated antibiotic use can cause the adult teeth in the gums to discollor. You really should push to find the cause of the problem and have that treated. The sooner the better.
With that many tonsilitus infections in sucha short time, I would definitely consider getting his tonsils removed.
It's possible that part of his problem IS allergy related, so starting off with some allergy testing may be another route - would be less invasive than surgery. If it turns out that he has a lot of allergies (other than the milk that you mentioned), then getting GOOD treatment for those may improve his tonsil issues.
Unfortunately, chronic use of antibiotics can actually make things worse. Our bodies find a way to "get around" the antibiotics and they become less and less effective, therefore, although the symptoms may go away after a few days on them, the infection is still there and comes back quickly and with a vengeance after the antibiotics have been stopped.
Has he seen an ear nose and throat doc or just a regular general practitioner? If he has not been seen by an ENT doc, I would definitely suggest having him seen by one.