Dry leaves harbor mold spores. Antibiotics will not clear up allergies, but they will help if there is a secondary sinus infection.
Have you tried all of the different OTC allergy meds (Claritin, Allegra, Zyrtec, Benadryl)? It may be a matter of finding the one (or combination of a few) that is right for you. A steroidal nasal spray may also offer your son some relief.
Secondly I would recommend you see an allergist and ask about allergy shots. It is a process of desensitizing your immune system from the allergies that it feels are potential threats. It takes time to desenstitize your body but I can tell you that the process is MUCH faster in children that adults.
Singulair is not an antihistamine but a lucotrene (sp?) receptor. It is typically used in addition to antihistamines but works differently. (The allergist will need to determine why your son's heart races with the meds.)
I have heard of children having behavioral issues on Singulair. My daughter's experience was different. She actually developed joint pain all over her body. After a battery of negative bloodwork I suggested it might be the Singulair. She got off of it and all of the pain went away. All medications effect everyone differently. Just stay aware so that if you start to notice changes in your son you can discuss them with his doctor.