She looks like a Russian Blue. This breed is actually quite susceptible to feline hyperesthesia, which it sounds like may possibly be the case with yours, given the mention of the skin problem she has.
I had a Russian Blue a long time ago with this condition, and it was awful to see her outbursts. She would become very anxious and aggressive during these episodes, and would often start violently biting and scratching at herself, sometimes even attacking anybody who would try to help calm her down. But when the episode would pass, she'd go immediately back to her loving, affectionate self as if nothing had happened.
If you can, I definitely recommend getting her checked by a vet. Hopefully it's not feline hyperesthesia, but if so, there are medications that will help with it.