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There are a number of different things that could cause the signs you are seeing. We can see this with a tooth root abscess, nasopharyngeal polyp, tumor, or something as simple as an upper respiratory infection.
Since she does go outside, it is possible that she has been exposed to something infectious form another cat in the neighborhood.
I recommend having her evaluated by your local vet. I would start with a physical exam, including careful exam of her eyes, teeth and throat. If everything appears normal, we can try an oral antibiotic as well as an appetite stimulant.
Aside from that, you can try warming her food. Try canned cat food, canned tuna, or even meat baby food to entice her. You can also sit in a steamy bathroom with her to loosen any respiratory secretions and relieve congestion. If she can smell her food, she will be more inclined to eat.