Zoey was the same way when I got her and she was already 11 months old!! In fact this is why she was at the pound, surrendered by her owners
I was so frustrated because I thought there will be no way I can change her ways. She was really sweet and affectionate when I'd come home from work or get up in the morning but the rest of the time, she was playing, and I couldnt even pet her or come near her with my hands because she thought they were toys
Saying NO!!! firmly to her doesnt work.. but all cats are different. In fact it eggs her on, its unbelievable lol. I started using Flower Essences
.. about a month and a half ago and I swear to you, I have noticed an almost 180 in Zoey. She no longer tries to bite me any chance she gets, in fact she is WAY more affectionate, always constantly rubbing on my legs, talking to me, wanting to be pet and rarely bites me anymore. Just once in a while when she's really playing hard. It is really sooo much better than when I first got her.
Give it a try! I put 4 drops in her wet food twice a day everyday.