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Hello. Thanks for the question.
The most common cause of discharge and redness to one eye is a corneal ulcer or scratch to the cornea. That will lead to discharge, squinting and redness. It's diagnosed by doing a fluorescein stain test on the eye. An ulcer will pick up stain and show up under a blue light. The treatment is then with an antibiotic drop like Neo-Poly-Gram.
If the stain test is normal, it may be conjunctivitis. These are typically allergic in dogs. We treat with a steroid drop and it clears up quickly. Conjunctivitis is more often seen in both eyes, so if it's just one eye the ulcer is more likely.
Your vet should be able to get this diagnosed and treated fairly inexpensively.
I hope this helps, let me know if you have any other questions.