My cat seems to be swallowing really hard like he has a sore throat...

I have 2 indoor cats Bear & Lilly (brother & sister) , they are 1 yr and 4 mths old with all their shots and they are due for their annual checkup in about a month. Recently, my boyfriend brought in a stray cat probably about 6 mths old because of how cold it was outside and we know that cat at least has worms and obviously has never been to a vet. Well, now my Bear seems to be having a really hard time swallowing like he has a sore throat. He does try to eat but he seems to gag sometimes and spit up a little, could he have caught something serious from the stray or possibly from us? My boyfriend had a sore throat for a few days also...

Cats can catch sore throats from humans.  It's possible he either caught it from your boyfriend or the stray cat.  I would recommend a vet visit.

Is Bear any better today? Will Bear allow you to look in his mouth? There could be so many possibilities causing his difficulty in swallowing, let's hope it is just a little bit of a sore throat, but a vet visit is the best thing if it continues. Not to scare you, but if a kitty goes more than two days without adequate food it can turn very serious very fast. You didn't say if it was kibble or canned he was trying to eat? 

That was so very nice of you to bring the stray in from the cold.   

I noticed My cat got this problem from stomatitis. It looked like she was swallowing hard. You may want to look at the gums because infected teeth could swell the throat.