Tummy issues with newly adopted stray

Good day everyone! We've adopted our stray kitty about a month ago now. Since the beginning she's had tummy issues, having runny poop. We've fed her skinless boiled chicken for a while, then put her adually on kitten food, and when her tummy seemed better, normal kibble with canned. We've had her dewormed twice now, everytime after the deworming her poop would be more solid and healthy. But the runny poop gradually starts again after a week or so. Overall she seems healthy, playful,healthy appetite. We don't feed them anything inbetween, so they only get fed the kibble and the canned food now. It's definitely not something that can be catched by another cat, as our other cat Rasberry is completely fine. Also, the vet said it might be a parasite, but it wil go away. She didn't give me any medication for it. What could be wrong with her? Is there any medication I'd be able to get over the counter (at the vet's or otherwise). I'm putting her back (yet again -sigh-) on the boiled chicken. It doesn't really help, but maybe it relieves her discomfort.

Since deworming clears it up and then it comes back it sounds like a parasite.  I know there should be two or three dewormings done with a specific number of days done between treatments for some parasites.  Was the second one done after a few days or was it done when the symptoms returned?  If it was done because symptoms returned then they aren't being completely cleared up.

The second deworming was done more or less 2 weeks after the first. So then it didn't properly clear up. The poor thing. What kind of parasite would cause this? And is this thing serious? I'll have to take her in to the vet in any case. Do vets give deworming pills over the counter? I'm just thinking this girl will HATE driving to the vet every few days for deworming lol! Or must they give the animals the medication themselves?

My vet gave me all of the doses and instructions on when to give each one.

Thank you very much for the advice, I'll make a turn at the vet's tommorrow. This helped a lot!