You are right: viral infections cannot be healed by antibiotics but many viral infections have bacterial infections on top. As soon as the liquid coming from the nose is white greenish (and no longer clear) it means there are leucocytes in -the immune system is fighting bacteria.

Cat "colds" can have many different reasons and can be very dangerous. So it's anyway better to see the vet. I hope that in your area you can find a vet who uses more homoeopathic stuff or other meds that are not as heavy.

I wish your cat all the best. And welcome at PT!