There are plenty of great over-the-counter options. Zyrtec went off the prescription list about 7-8 years ago. Another popular option is claritin. If oral anihistimine is insufficient, you can add Nasacort or another brand nasal spray, many of which are over-the-counter. We get Nasacort via prescription because it's cheaper that way. Pediatricians are really far more comfortable dealing with hay fever than food allergies and would probably send over a prescription without another visit.

Hay fever can definitely make kids behave in annoying ways. You might want to limit outside activities during high pollen times of day.