May God bless you for aadopting an adult shelter kitty!!
He should gain weight under your loving care.
URIs are quite common in shelters as they are airbourne virus.
All cats carry upper respiratory virus on their own fur. Cats that live together become immune to the carried strain but as soon as the bacterium is exposed to another cat it will infect them. If this baby was exposed to other cats he likely contracted it from them or stress.
Feed him very odorous food so he can smell it and will keep eating. If he gets dehydrated, give him a few droppers of unflavored pedialyte througout the day to hydrate him and balance his electrolytes.
H e can have an OTC called clortrimeton - a quarter tablet every 12 hours if he is congested. You can also take him in a steamy bathroom where you have run a hot shower to break it up.For the eyes get Terramycin ointment. some pet supplies have it but call first or order from http://www.revivalanimal.com/
Apply a damp teabag today for 30 seconds 3 times.
If he develops any colored mucus that means the infection has turned bacterial and will respond to an antibiotic.Some vets script one even if it is viral to prevent secondary infections like pneumonia.
Please let me know how he is feeling. If you get worried I will always be here to help further.
I hope he feels better very soon.