Hi, Ash A! Welcome to the board!
Worms are pretty common in pups and kittens, so it sure wouldn't be unheard of for your guy to have them. The only way to know for sure is to have a vet look at him. Over-the-counter wormers aren't very good at best, and at worst might harm your kitty, and you don't want to unnecessarily medicate him. So your best bet is to make a vet appt.
Depending on the type of worm(s) he might have, better to get it done sooner than later--some might cause permanent damage, and some can be passed on to you and your family.
And, when you get time, we'd love to see some pics of your kitten!