They will most likely give him antibiotics for secondary infection.
If he's eating and drinking, then no need to take mayor action, but if he gets so congested that he can't breathe, or stops eating or drinking, then take him to the vet, right away. Kittens can fail very quickly.
If he gets congested, try a nice 1/2 hr steam in the bathroom. Don't leave him alone.
If he is just sniffly and has runny eyes, then the URI is probably mild.

Please ask you vet for advice over the phone, if you can't get an appointment.