I would not recommend over the counter wormers...for one thing, unless you are familiar enough with every worm to correctly identify what your kitten has, you need to take in a stool sample to your vet for them to identify exactly what your kitten has, and to then give you an effective medication guaranteed to take care of it.
Depending on what kind of worms these are, will affect what you need to do. I would seperate the kitten from your other cat until you know exactly what kind of worms...they should have seperate litterboxes. I'd get a new one for your cat, use the one they'd shared for the kitten *just* until you know what kind of worms..if tapeworms, i'd keep this old box, but if round worms, frankly, I'd ditch this box as soon as the kitten is being treated.
Roundworms can be contagious via a shared box, tapeworms means the presence of fleas and unless your cat is on a flea tx such as advantage which would protect it against any fleas the kitten might have brought in (*if it has tapeworms, it has fleas), you'll need to have both the kitten and your cat treated for fleas, and use a safe tx for your home.