Cat with Roundworms, Help!

So I am a new cat owner.  I adopted my little guy Oliver around 4 weeks ago from the Anti Cruelty Society.  He is super cuddly and playful.  I even call him a stage 5 clinger because he is basically attached at my hip when I am home.  Today though he threw up and there was a worm in it!! I wasn't that freaked out until he threw up a second time and there were A LOT of worms in it.  I called our vet right away and picked up a dose of Strongid which I gave to him asap.  

Just a little bit of pre-history:  My cat is indoors only.  I am a pretty clean cat owner, I clean his litter box every other day and I hadn't seen any worms in his feces.  I also vacuum around his litter box every other day to grab any litter he spills.  I am also a nurse so it takes a lot to freak me out but this has me totally losing it as I read that roundworms can be spread to humans.  Since my cat is so cuddly I am super worried I could have contracted these creepy things from him.  I always wash my hands after cleaning his litter box and when he playfully nibbles on my hands.   But I'm sure there have been times I have petted him and held him without washing my hands after?  The worms he threw up were adult ones so they have obviously been growing for a while.  He sleeps on my bed at night and sometimes even on my pillows.  I also sometimes find him on my counter top or on the table.  I read that the eggs can be deposited not only on feces in the litter box but also on surfaces the cat frequents.  

Like I said, I am a clean person but I am freaking out about these things.  What are the chances I could be infected?  Also, should I not let him on my bed and places until after I'm sure he's not infected with them?  I am also racking my brain thinking of where he could have gotten them, as I was assured he was dewormed when I adopted him a month ago?  

Any help or advice would be greatly appreciated!!

I found this for you:

http://cats.lovetoknow.com/can-humans-get-worms-from-cats

From my understanding from this site Kittens can get worms from nursing from Mom. You need to deworm at 6, 8, 10, 12 weeks then again every three months. But there is flea topicals that take care of the fleas, worming and ear mites. When your baby is old enugh for it ask your vet. 

taylorkay410 said:

 
Any help or advice would be greatly appreciated!!

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You're not going to get worms and i wouldn't change anything with respect to him and where he goes except that of course he needs de-worming with prescription medication from a vet (not from the pet store) and your adoption center may help you with this.  Many cover pre-existing shelter related conditions and he clearly had the worms at the shelter and wasn't fully de-wormed.  They would be my first call.  Try and collect a sample if possible or take a photo.

You won't get worms from him. I've been rescuing feral cats and kittens for years and they pretty much all have round worms, but I've never had them. It some times takes a couple of doses of worming medicine to get rid of all the worms and eggs. 

You can take a stool sample to the vet and they will check it and let you know if he still has any eggs in his system.

Make sure you only use the worming medicine you get from the vet on him. The over-the-counter ones aren't any good and can cause allergic reactions.