Hi, Melanie and welcome.
I'm sorry your cat is experiencing this problem with frequent sneezing. It's possible that he either has an upper respiratory infection (URI--kitty cold) or allergies, and this is what's causing him to sneeze. The slight blood that you see, may be due to the dryness of the membranes inside his nose and irritation from sneezing so much. Here is more information about URI's and allergies in cats:
I'm not surprised he won't let you wipe off his nose; most cats don't allow this and don't understand it's for their own benefit. It's instinctive for him to lick his nose until it's clean. Just watch that he doesn't make a sore on his nose, from the excessive licking. If this happens, apply a thin film of plain Neosporin (it won't harm him to lick it).
I recommend using a humidifier in the rooms where he spends the most time, as the moisturized air will help with the sneezing. You can also run a hot shower to steam up your bathroom and sit in there with him for about 10-15 minutes, several times a day. Also, if you use air fresheners of any type, stop their use, as it may be irritating him and adding to the sneezing. If anyone smokes in the house, stop that, too and try not to use strongly scented laundry detergent, fabric softener, cleansers, scented candles, etc., in your home. Make sure his litter is low dust or dust free and is unscented, as well.
It would be advisable to have him evaluated in person by his vet as soon as possible, to determine if this is an upper respiratory infection, calici virus, allergic rhinitis or another condition. URI's that are viral, just like our human colds, usually run their course within about 10 to 14 days. Unless the mucus is colored green or yellow, indicating bacterial infection, antibiotics are typically not needed; however, some vets like to prescribe an antibiotic like Clavamox (or others) as a preventative against secondary bacterial infections.
An antihistamine might also help and until you get him to the vet, you can try 1/4 of a 4mg. Chlor-trimeton tablet every 12 hours. It's a tiny pill, so 1/4 of it is really small; you can hide in a small amount of wet cat food you offer from your hand, or a soft treat like Pill Pockets by Greenies. Follow it with some more food and water, to help wash it down. Here is more information:
If your kitty begins to mouth-breathe and/or stops eating or drinking, he's lethargic and his eyes become runny, an ER vet visit will be necessary to get a definite diagnosis and treatment.
I hope your furry boy is feeling much better, very soon!
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