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The eyelid swelling and fever might be due to a mild abscess or infection in the eyelid area. You did the right thing in giving tylenol. Also apply warm compresses on the affected eyelid if the child allows. If the pain is not relieved by tylenol, then you can give ibuprofen also. She would need antibiotics orally as well as eye drops to cure the infection, so an evaluation by her doctor as soon as possible would be ideal.
usually an infection to get transfered from animals and the symptoms to appear take 2-3 days. The exposure to animals seems like an unlikely cause. Children tend to rub their eyes with dirty hands (after playing etc) and can land up with such infections.