Please help.. randomly aggressive cat

Hello all, I need some advice as I am about at my wits end with our new cat. About two and a half months ago we were walking downtown going to dinner when we came across a cat who was stuck and crying out to us. I helped her out and she followed us around meowing, plopping down showing us her belly, and being really affectionate. She was pretty thin but very affectionate so I didn't think she was wild and decided to take her in. We posted flyers online and checked ads and no one claimed her. We took her to the vet and she didn't have a microchip and was about 7 months old. She got her shots and we got her spayed. Everything was going great at first. She was very sweet but this past month that has changed and it's only getting worse. She still acts affectionate but will claw and bite me randomly now. She attacks me when I walk around my house (which isn't a big house so basically anywhere I go) and I'm not sure what to do. Here are some scenarios. When I wake up and walk to the kitchen she plops down in front of me and shows me her belly making meows and rubbing up against my leg. If I pet her I have about a 50/50 chance of being bitten or scratched right away. If she doesn't bite me right away if I pet her for about a minute and then walk away she will jump on me with her claws and bite me. No matter if I don't react or give her a firm NO she will wind up again and jump, claw, and bite me. I then say NO again and she really goes crazy the third time, really trying to hurt me. I never physically punish her or intimidate her, I try to be understanding and want her to feel better about me and not be afraid of me (not that she is afraid but I'm trying to understand why she attacks me) but it's not working. Second scenario I'm just walking somewhere in my house. Multiple times a day she will jump on me with her claws and bite me, often a few times in a row getting more aggressive each time. At first I thought she just wanted to play, so I played with her two times a day for about 10minutes and got her one of those automatic pully cat toys that she can chase. That helped a little bit when she gets tired but she still attacks me when she gets more energy. Third scenario we are sitting on the couch watching a movie. She cuddles up next to me and I think "finally, we are making progress" when out of no where she grabs me with her claws and bites me! I'm tired of being attacked by her in my own house. She always has food in her bowl, clean water, and I even play with her. Her behavior is erratic where she seems so sweet and then attacks me. I feel bad about rehoming her if she is just going to terrorize the next family and I feel bad about returning her to where I found her because she was so thin. But I can't continue to let her attack me in my own home. I'm hoping someone on here can give me some advice. Also I used to have two cats and my wife had one cat in the past so we have a decent understanding of cats.