Assuming his eyeball is red, with mucus, Polysporin works quite well. You can purchase this over the counter at any drug store. You can purchase Polysporin in drops or ointment (looks like Vaseline).
The ointment I believe works better. It works well on Dogs and Humans to clear up conjunctivitis. Give your vet a call though, and ask if you can try it on your Hamster.
It's just a phone call. If you decide to try the Polysporin, (after you talk to your vet), sooth his eye with a warm damp washcloth and keep the eye clean of mucus, before you apply ointment. Only apply ointment once a day.
YOUR HAMSTER MAY HAVE A RARE DISEASE THAT MAY NEED SURGERY (MINE DID) What you need to do is go to a pet store and ask what they would say to do. Then call 1800PETMEDS and order an eye drop prescription. After that you need to call your vet for tips how to put the eye drops in.
Some hamster's eyes are naturally red but if you see anything abnormal about his eyes besides them being red you may want to take them to the vet. I wouldn't suggest using creams or topical's because the hamster can lick it off. If a hamster licks off creams it can be life-threatning.
The best thing to do is probably to take the hamster to a vet or a local pet store and see what they say.
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