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I sounds like a upper respiratory infection. This needs to be evaluated by your local veterinarian for antibiotic therapy.
AS for the heat question. A female can go back into heat as soon as she weans the kittens. I mean with in 24-28 hours.
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It is possible that this is allergies. However cats show signs and symptoms of allergies in their skin more than in the respiratory system like we do. Its more likely your cat is dealing with a viral or bacterial infection. You can use saline eye wash to try to rinse the eyes out but if the discharge returns she needs to see a vet.