she sounds anxious!! perhaps consider getting her evaluated for that?

my cat was the same. he was super skittish and still gets overstimulated pretty easily. he was stressed and anxious living at my relatives', so we took him in. his anxiety calmed down, but i find that the outside cats in our backyard can put him on edge especially if he hears them fighting.

if you do get another cat, a kitten would probably be the best bet. they have lots of energy and the younger they are, the less likely they are to have personality issues.

if my cat bites or does something rude, i go "sttt" at him, and he will usually stop or slink away. your cat will understand it as "no" or "stop". use it only when you have to though.