I am so sorry your baby is not feeling well.
She most likely has an URI:
Yes cats can take amoxi @ 5 mg per lb every 12 hours.however, they dont cure anything viral:
All cats carry upper respiratory virus on their own fur. Cats that live together become immune to the carried strain but as soon as the bacterium is exposed to another cat it will infect them. If this baby was exposed to other cats she likely contracted it from them or stress.
Feed her very odorous food so she can smell it and will keep eating. If she gets dehydrated, give her a few droppers of unflavored pedialyte througout the day to hydrate her and balance her electrolytes.
She can have an OTC called clortrimeton - a quarter tablet every 12 hours if she is congested.
You can also take her in a steamy bathroom where you have run a hot shower to break it up.For the eyes get Terramycin ointment. some pet supplies have it but call first or order from http://www.revivalanimal.com/
Apply a damp teabag today for 30 seconds 3 times.
If she develops any colored mucus that means the infection has turned bacterial and will respond to an antibiotic.Some vets script one even if it is viral to prevent secondary infections like pneumonia.
Please let me know how she is feeling. If you get worried I will always be here to help further.
I hope she feels better very soon.