Welcome to TCS! You have found the right place to learn all about your kitty and to ask ANY questions you've got about your kitty's health or behavior (or just share pictures.
I've never heard of a human getting round worm from a cat. I suppose it's possible... but it would be difficult - they have to be ingested.
But I'd think a good percentage of us have had cats with roundworm. It is very common with outdoor kitties or rescue kitties! If your cat is indoor only, it should not be an ongoing problem. If your cat is indoor/outdoor, your kitty should be treated either with Revolution or Advantage Plus (a liquid you squeeze onto your cats' skin between the shoulder blades) to kill fleas, ticks, and most internal parasites (including the two most prevalent, round worm and tape worm).
I don't know which med your vet gave your cat. If she gave your cat Drontal (a pill), I wouldn't trust that the round worm is being treated. It's usually done with Panacur or StrongidT (those are the brand names - your vet may refer to all of them with their generic names). Either of these usually require being given to the cat each day for 10 days.
Any deworming med is actually a poison - and all of them kill only the adult worm. So any deworming must be done again - some vets use 2 weeks as a guideline, others use 3 weeks. We do it after three weeks.
During the entire 5/6 week period (10 days of initial meds, three weeks of waiting, another 10 days of meds), it is a really good idea to empty the litter boxes completely each week, bleach them, and refill them with all new litter.
Also, scoop as often as you possibly can. The cleaner you keep the box, the lower the risk of reinfestation. (Cat jumps into box that has poop in it, cat moves litter around, gets worm egg from poop on foot then cleans itself...)
If you scoop frequently, bleach the boxes weekly, and administer the dewormer again in 2-3 weeks (unless the vet used Revolution or Advantage Plus - then it should be administered again in one month), you should have seen the last of the problem (if your kitty is indoor only).