Technically your vet is doing the correct thing. Your kitty most likely has Feline Viral Rhinotracheitis (a kitty cold) and therefore like a human cold it has to "run its coarse". It is a virus, so an antibiotic will not help. Like your vet explained, if there is drainage, not clear, but dark yellow or brown like mucus, then that suggests an infection. At that point, an antibiotic will clear the infection and the virus itself will still pass on its own. As long as your kitty is sneezing clear fluids and has clear secretions from her nose and eyes, there is no infection for an antibiotic. HOWEVER, you can ask for some L-Lysine to use as an immune booster / supplement. It is usually sold in tubes! If your regular vet doesn't sell it, you might be able to find it at another local vet or Co-Op.
Good luck and try not to worry! ;)
Kim