Can you be suddenly allergic to aspirin?

Aspirin allergy: Allergic reactions to foods & medicines can develop "suddenly" without warning, even if the particular substance has been consumed before without any difficulty. Aspirin allergy can begin unexpectedly but it is also important to rule out another kind of adverse drug reaction such as a predictable side effect or an idiosyncratic response; these reactions can occur inadvertently and not every time.

Yes: Allergies can develop at any time even if you have been taking the medication regularly. Allergy can be confused with adverse reactions and i recommend evaluation by an allergist if you believe you have developed an allergy.