The right way to treat swollen eyes is first to determine the cause of the swelling because otherwise you risk making the problem worse. For example, if your cat has an infection caused by a micro-organism other than a bacteria, using an antibiotic eye ointment is a no-no, as is using an ointment with a steroid/cortisone if there's any damage to the cornea. If gently rinsing the eyes and then applying warm compresses several times daily does result in a decrease in swelling within 24 hours, your pet really ought to be seen by someone who can determine the cause of the problem and the correct treatment for it.
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diagnosis, or treatment. Never delay or disregard seeking professional medical advice from your
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If you have a medical emergency, call your doctor or 911 immediately.