Sneezing Kitten

I visited a friend today who'd recently adopted a kitten from a shelter. She says he's ten weeks old, he's already been neutered, and has received his rabies vaccination already. Anyway, while I was there, I noticed he's sneezing very frequently. Also, his eyes looked watery to me. She said he's been sneezing from when they first got him. I also noticed while he was eating when he stopped to swallow it just didn't sound right to me. Maybe I'm just thinking too much about it, but I encouraged her to take him to the vet to get checked. I was wondering though if anyone here might have some idea of what could be going on. Otherwise, he seemed pretty normal. I watched as he played for a while.

He most likely has an upper respiratory infection. A trip to the vet would be the best thing. Its common for kittens and cats to get. Just try to encourage her to take him.

It's so very common for kitties in new homes to develop an upper respiratory infection about 10-14 days after coming home.  I would encourage her to take him to the vet for a check up.

I did hold him for a bit , but I did wash my hands when I got home. Is there much chance of me passing it to our own kitten that's about 3 1/2 months old from holding the other for a bit and petting him?

It is good that you washed your hands when you got home.  I have a friend who has multiple cats and she always washes her hands when she comes over to check on my cats when we travel.  Her cats are healthy but is just a precaution that she takes.  I often do the same thing when I come home after visiting her house even though all of our cats our healthy.   She has been around my cats when they have had URI's and has never brought them home to her cats.  She actually helped me medicate one of my cats when he was being difficult.