Biting and barking

Hello,

I've recently purchased a female Jack Russell puppy who is only 8 weeks old and it is only her 4th day home.

She's adorable and wonderful, but sometimes her biting is too rough and I worry that she will not know her own strength. I know she is still teething, but when she does bite, I think she thinks we are playing and doesn't stop. I've hit her across the month when that happens and say, "NO!" but lately, she's been snapping back and trying to fight back. I then give her time-outs for a minute or 2, where she constantly whines since she doesn't like to be left alone in a room.

When I come back, I'm not sure what to do next. pet her to make she sure is okay, or just ignore her?

This is my first puppy and sometimes her biting scares me. I just enrolled her in puppy school and will start in the next 2 weeks.