Sudden cat aggression

I have had my cat for a few years now and she's always been the only cat and strictly indoors. Yesterday I brought a new cat into the household because I'm cat sitting for a friend. They just stared at each other for hours at first and then the new cat starting messing with my cat and taunting it, and then they moved onto growls and hissing. They spent the whole night taunting each other. My old cat would hide behind a doorway and pop out and hiss when the new cat tried to get through the doorway. Today it came to a point when I was holding my old cat while walking through the kitchen and she saw the new cat eating out of her food dish. The old cat started hissing and swatting at the new cat and when I tried to calm her down the old cat started hissing, swatting, and biting at me. I ended up bleeding from her scratches and was so angry I ran after her and she jumped into a closet and sat there and hissed at me. I tried to pick her up and she swatted at me again. My cat has never shown aggression towards me like this before. I'm actually kind of scared of her. Is she going to kill me in my sleep? Why is she showing aggression towards me when it's the other cat that bothers her? How can I fix this problem, I want them to get along while the other cat is here.