Threadworms/pinworms are very common (everyone has or had them). Others - roundworm, tapeworm) are not rare. If you haven't been treated for them then you've got them - at least threadworms, maybe others.
There are medications available from pharmacies without prescription - just buy and use what will treat the whole family. Talk it over with the pharmacy staff if you don't know what to do - like I said, EVERYONE gets them, particularly young children - no need to be bashful. No exceptions - everyone at once - and that includes the pets. Then do it again at the recommended spacing. Thereafter you only need treat (the whole family) again when someone has symptoms.
And make sure THE WHOLE FAMILY follows solid hygiene practices - always wash hands after toilet, after contact with animals, before food (either preparation or eating). Another type of worm is hydatids - easy to get, potentially horrible - read up on it so you know WHY you should practice hygiene and worm pets regularly.
But I don't think you need to worm people except initially and when symptoms show.