Redness, swelling and hair loss around the outer ring of a dog's eyes may be caused by a variety of reasons, including but not limited to eye infections, skin diseases, allergic reactions, etc. Here are some possible causes and their corresponding treatments: 1. Eye infection: Eye infections in dogs can cause redness, swelling and hair loss. Treatment usually involves the use of eye drops and ointments to reduce inflammation and promote healing.

2. Skin diseases: Such as fungal infection or mite infection, which may cause redness and swelling of the skin around the dog's eyes. Hair removal. Treatment usually involves the use of antifungal or antimite medications, and possibly topical medications. 3. Allergic reaction: If your dog is allergic to certain substances, it may cause redness, swelling and hair loss around the eyes. Treatment may include avoiding allergens and using allergy medications.