It depends on what you're allergic to and where you live.
If you have seasonal allergies or hay fever, tree pollens can trigger symptoms in the late winter or spring. Ragweed releases pollen in the summer and fall. The specifics also depend on where you live. Allergy season can start as early as January in Southern states and linger into November.
The key is to see your doctor and find out what's causing your symptoms. Once you do, you'll know when your allergy season starts and how to prepare.