It is important that you and your veterinarian react quickly in order to try and save the hamster's eye(s). Eyewash will first be used to remove any impurities; your veterinarian may then administer agents such as pilocarpine to reduce the pressure buildup in the eyeball. Other medications commonly used for exophthalmos include anti-inflammatories and corticosteroids -- and when the eye protrusion is due to an infection, antibiotics. Unfortunately if the condition worsens, the eye(s) will require surgical removal.
Place your pet in a calm, dark environment -- and away from others pets -- during the recovery process to reduce its activity. If the eye has been removed, a patch may be used to cover the exposed wound. A post-operative care schedule and regimen will be given by your veterinarian.
Promptly separating fighting hamsters and learning the proper way of handling such small animals can reduce the risk of exophtalmos due to trauma and improper handling. Eye infections should also be treated quickly to prevent it from further worsening.
The displacement of the eye