Found starving cat purrs, swats and bites

I have a young cat around 4-5 months hanging around my house, I was able to pet it once and realized it was starving, just skin and bones. I started feeding it and couldn't even come close to it for another 2weeks. Then I caught it and put it in my shed with food water and a very comfy warm set up. The cat purred, chirped, meowed and rubbed on everything. I was able to pet it and it seemed to love the attention. I had my mom come over who has lots of experience with cats and is a retired vet tech to check it over. The cat was very lovable with her as well. It wasn't til the next day when I went in to feed it and was petting it while it purred,(not while it was eating and it already had a full belly) without warning growled and bit me. I thankfuly had a coat on and was quick enough to pull away before it could really sink it's teeth into me. It continued to purr and growl and back up in an aggressive posture, I also backed up calmly away from the cat, when I turned to leave it launched at me and grabbed my ankle. After discussing the incident with my mom we came to the conclusion that it might of been the wind storm that set it off from the night previous. The follwing day I went in and fed the cat, it seemed happy to see me purred and was rubbing on stuff again. I made sure to pet it very gently this time and only on the head. I put my hand on a chair that was in there to invited the cat up, not tapping or slapping the chair very non-threatning manner, instantly it swatted me and started to growl and purr and began backing up again. I left before it took it any further this time without turning my back to it. The cat is a classic tabby. I already have a cat and two dogs. It met the dogs without fear, never met the other cat. The cat is free to leave if it wishes so it's not stressed by being confined and it knows this area very well. I also have a son I am concerned about after seeing this behaviour, it's cold here and I was going to bring it in but am unsure. I don't have a separate room to put it in, it would have to be with the family. I am concerned this cat is a ticking time bomb and could never forgive myself if it attacked my son and permanently scared or caused nerve damage from a bite.I have been involved with animal welfare for years and have taken in many cats, I have only seen this behavior one more time with a cat that attcked someone so bad they needed medical care. I've encountered other behavioral problems but not a cat that is freindly and purring and attacking you at the same time. Any suggestions from anyone?????

Thanks for the reply, I am very cautious of the cat. The tail never gave any indication it felt threatened or was going to bite. If I had a quiet home it would be better for the cat, unfortunately for the cat I have a small house that has alot of noise and 2large dogs and a noisy siamese mix cat and a son and husband that aren't so quiet. If I had a spare room it may work out for it. I'm going to try and see what I can do for her. Thanks

Oh yes, there was an appointment made before she even started doing this weird behavior.Either way if she's not a good indoor pet cat then, I am willing to keep her as a garage cat. We will be instaling an old propane camper heater and a kitty door in the shed. When I check on her the water dish inside isn't freezing at all so it's pretty warm. She has fattened up some from feeding her for the last 3 weeks, and she will continue to get fatter as the days go by. And althought idealy a cat on a couch is the best, she's got a way better situation than she had before. Some cats I think just prefer the handout, a light pat on the head every now and again and that's it. Especially if they've spent most of their life as a stray, maybe too much contact is too much for her.She'll have her shost, deworming and spay, so if she chooses to stay or leave she won't reproduce and have other kittties suffer the same fate. It's a shame how many times people have to shell out time and money for someone else's bad decisions.