You have a very young, baby on your hands. Is she fully weaned? Or eating food yet? It does sound like if you did not get her when you did she would have died.
I think the vet gave her shots anyway, because of being in such a high risk of catching viruses .She was not from a good home.
However, there a a high chance that the vaccines will not work . IF the mother's immunity blocks out the vaccines, this is going to be ineffective. Poor little puppy was so infested with fleas, and worms
I am glad she is in good hands now .Congradulations!