I am so sorry you are having this trouble, especially with a kitty you were so kind to rescue!
She should be checked by a vet to make sure she is not in any pain as that can cause sudden aggression.
If she is found to be healthy, she may just want to play and the 13 year old kitty does not want to be bothered.
Your cat may just be a bit hyper. She has what we call misdirected aggression however, her behavior is not actually meant to be aggressive. She is treating humans as though they were other cats..So to stop her we must act the exact same way as another cat would treat her
This is the way cats act when they play with other cats -they have a specific language they use to communicate with each other.
You do not need a behaviorist for cats. They are really quite easy to understand.
They do not rationalize, nor are they capable of in depth thought or reasoning.
Everything they do is basic, logical (to them) and makes perfect sense.
In a cat hierarchy a strong kitty will always try to take over and assume the head cat position. In addition, that is always subject to changes if cat one senses weakness in cat two. Cats DO work things out in their own way and they could care less what humans (or behaviorists) think. They only respond to the energy of another animal be it feline, canine or human. Punishment is useless and counterproductive because they simply do not understand being hurt - they would just try to avoid the hurter in the future but it would not teach them anything.(except fear)
Cats do not follow a pack leader the way dogs do but they do sense their human parents energy and respond accordingly - so if you are nervous, they will be nervous. If you are stressed, they are stressed as well.
DO NOT ALLOW HER TO BITE - NOT EVEN ONE TIME!
If SHE gets aggressive - just say SHUSH and tap her very lightly on the head. That lets her know (in a cat way) that the behavior is unacceptable and she will understand that feline method of correction and not be hurt, upset or insulted.
Do not yell, spray water or act upset, Just immediately calmly and firmly correct her . This will teach her that his aggression will not be tolerated the way another cat would treat her - except the NO! would be a hiss and the tap would be with a paw. Consistency is the key here.
Get a brand new feliway plug in and rescue remedy at a pet supply to safely keep her calm.Use rescue remedy on the gums.
Please let me know how things are going. If you have questions along the way I will always be here for you.
I will help you resolve this so you can have peace in home so dont worry. Things will be fine -I promise.
Just remember to be CALM all the time!
Warmest best wishes,