Is it really too hard to pick up some Advantage or Revolution and dose the cat? As for the house, vacuum EVERTHING and chuck the bag in the garbage outside when you're done. Buy a premise spray and don't forget to treat the baseboards, fleas love to hide there. Treat it like a lice infestation and wash everything you can in warm water if possible. If you think you're itching, imagine how the cat feels. It's probably losing fur and becoming anemic as you complain.

Shelters are often overrun with animals, and the ones that need medical care or extra attention like this one can't be taken care of properly since most shelters don't have the funding or volunteers. And no one wants to adopt a sick animal, so she would most likely be euthanized (unless it's a no-kill shelter, which those are often full and you can't leave an animal there).