Are worms a serious medical condition for my pets?

I am scared for my new labsky puppies. I think that they might have worms, but I don't have enough money to take them to a vet. I have been looking up symptoms for worms, and both of them have had them. One of them has a pot belly, he is very hungry all the time, and one night, he threw up 5 times! (But i think that is because he ate an old Hot Pocket he found under my sister's bed) The other one is very skinny, and he doesn't have a big appetite. Either of them has visible worms in their bile, but I think they possibly have worms. What kind of worms do they have if they do have them? And are worms a serious medical condition? And how can I treat them without going to the vet? Oh, and also, the one with the pot belly has a ringworm on his chest. The other had it first, and his went away once the other one got it. What does this mean? And how do I treat a ringworm without going to the vet?