J.M.
I too would say allergies. I have them and get weekly shots.
Try using a washcloth with mild soap and rinse them well. Also avoid eye touching (I know a 3 year old will touch everything). If you have animals after they pet the dog/cat wash their hands. Avoid what you can. If that doesn't work after a few days then ask your Dr and see what can be done. I know my daughter got tested for allergies at age 4 from a blood sample and they said when she is 5 they could get a better reading if she was allergic. She didn't have anything. My 7 year old doesn't show signs of allergies. Try the washcloth thing for a few days then go from there. Good luck!