Swelling and inflammation of the eyes is called conjunctivitis. It may be an infection of just the eye, often caused by bacteria, or it may be a sign of a more widespread respiratory infection.
Inflammation of the internal structures of the eye is called uveitis, which may be a sign of a generalized disease. If the inflammation goes untreated, it may lead to the formation of a cataract in the affected eye.
If you notice any swelling, redness, discharge from the eye, excessive blinking, or holding the eye(s) closed, you should consult your veterinarian immediately for treatment. Most eye infections can be treated successfully with antibiotic eye drops or salves.