My Mocha Bean does the same thing about once a year. Mostly in the Summer... maybe Spring. She is an Indoor ONLY cat. She is also allergic to Carpet Fresh so we don't use that on the carpets anymore. She gets itchy skin and a "weepy" eye. I just keep an eye on her to make sure its nothing serious .... I am OVER protective and panic at everything......... So to answer your question, yes I think Cats can have allergies.