Hi, I'm Dr. Deb. I will do my best to assist you today.
As you probably know, most upper respiratory infections
are viruses which do not respond to antibiotics.
There can be a secondary bacterial infection in some cats/kittens which is when there is a green or yellow or mucoid component to a nasal discharge (when they sneeze) or to an eye discharge. This is when antibiotics are used.
To answer your specific question, yes, penicillin can be used in a kitten but it is not considered the best choice for an upper respiratory infection. Better choices would be Clavamox, or Doxycycline or Clindamycin or Zithromax. If you don't have access to these antibiotics, Penicillin could be tried but you shouldn't be disappointed if it doesn't seem to help. This drug is dosed at 5 mg/lb.
The dose for a 1 lb kitten, for example, would be 5 mg every 8 hrs; you would be using an almost infinitesimal amount from a 250 mg tablet.
I'm sure you are already force feeding if your kitten isn't eating or drinking.
Keeping the nasal passages clear is also important. Nasal saline sprays from your local pharmacy can be used which clears the nasal passages, improves breathing and smell making it easier for the kitten to want to eat properly.
With supportive care, most kittens will get past an upper respiratory infection.
I hope this is helpful, but if you have more questions, please let me know.