Cats suffer from upper respiratory virsuses and they are not responsive to antibiotics. Actually the fact that your cat is not blowing yellow nasal discharge all over does signify the antibiotics are doing something.
My recommendation is to let it ride out its course. There is nothing additional that can be done, since you have the cat on medication. It may be an allergy, but I am guessing a virus from the other cat.
Sometimes it can take 14 days for these infections to run their course. If your cat has increased efforts to breath, stops eating, or develops significant nasal discharge...a return visit to the vet is needed.
Let me know if you have further questions.
Dr.Vamvakias
Cat Answer Team
Cat Expert
You are most welcome.
Good luck!
Dr.V