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For tonight, you can use pediatric nasal saline drops in each nostril to help clear the mucus. You can also keep running the humidifier if it's helping.
MOST cats that come from shelters DO have upper respiratory infection and they need antibiotics. This is not an indicator of how clean the shelter is but is just something that they fight every day.
You need to see the vet first thing tomorrow so that you can start antibiotics.
Let me know if you still have questions.
You should just tip the head back and drip them in.
Let me know if you don't understand.