"causing more damage" --- it can block passage of air, but what do you mean by damage?
see an allergist for your son's allergies. shots (desensitization) can help. medicines can help, such as antihistamines, singulair, nasal steroids.
Enlarged tonsils and adenoids could have an impact since they can obstruct the airway.
Removal of the tonsils and adenoids won't change his allergies.