We took in this stray cat several months ago because she was so
friendly and sweet.  I've had her spayed, shot, built her a house on
the deck, bought her toys, and she gets lots of love and attention.

Over the past week or so, she's started biting.
I've never had a cat before, so I don't know the behavior, but one of
the neighbors says she's just playing.

But she bit my son on the arm and made him cry.
When we try to pet her, she constantly nips at our hands.
It's very annoying, and I don't appreciate it.

Has she gone mad?  Is she playing?  And if so, how do we show her that
we don't enjoy this kind of playing?

My neighbor is a doctor, and he says that a cat bite to a knuckle or
any other joint is prone to very painful infection.