I've always put "mild seasonal allergies" on my medical stuff and it's never been an issue. I might have been asked once or twice about it... never tell them more than they need to know. I'm currently taking free flight doc prescribed claritin and flonase, and all I had to do was make an appt. to get them.
Where did you read you can't have allergies? I think what you read might be old. I know that's an AF thing, but I'm pretty sure seasonal allergies, as long as they're correctable by claritin/allegra and flonase, currently doesn't even require a waiver in naval aviation (although one time it did, I believe).