Coccidia is a very very common cause of diarrhea in kittens and no, you don't have to worry about getting it.
If that is the problem your vet will most likely prescribe Albon. It's a yellowish thick liquid like medicine that it easy to administer.
I've had similar situations with kittens I've fostered. They originally come up negative because it wasn't detected in the fecal. Also what can happen is the kitten can have eggs in the poop, which gives you a negative fecal but those eggs are going to hatch and now your negative kitty is a positive one.
VERY IMPORTANT...make sure to scoop the poop right after she does her business and change the box as frequently as possible. Since she is a kitten you might consider changing it every day as I imagine her box it pretty small. If she steps in her poop she can get reinfected since it is a parasite that the cat will shed in its poop.
So, make sure she stays hydrated, get a fecal done ASAP and if its coccidia, give the albon and make sure she has a super clean box!