How long has he had this? Is it only the right eye? Usually allergies will effect both eyes, one eye only would lead me to think foreign body (or perhaps unilateral entropian if he has always had it) As Carrianna mentioned, your vet would be able to tell you for sure. We can only guess.
It could be allergies even though it is on one side , but he also could have gotten something in it or even gotten a scratch which you wouldn't be able to see. The vet can put a stain in the eye and look under a special light to check.
Is it colored? if its green or brownish it could be an infection and would need a cream or some drops to help clear it up. If its clear could be allergies or something in it irritating it. You can try using a saline flush and just gentle wash it out see if it helps. You can also give benadryl if it clears up you know its allergy related. If it doesn't get better or has a color or thick look to it then go get it checked out.