Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that Angel is suddenly biting and scratching aggressively when previously she has always been a very gentle kitty.
Since this is new whenever we see a change in behavior, especially when a normally easy going animal becomes cranky, it is worthwhile to look for an underlying health problem. None of us is at our best when we don't feel well.
I recommend a physical examination, a stool check, mini blood panel with a T-4 (thyroid check) and urinalysis.
Many older cats develop hyperthyroidism (a tumor of the thyroid gland). This causes high levels of blood thyroid hormones which can lead to hypertension and headaches, which can make them very cranky.
At her age we cannot rule out organ failure and the elevated waste product levels changes their blood chemistry which can affect brain function.
Changes in hearing and vision can affect attitude too.
Arthritis can make simple touch painful.
And of course we also need to consider a brain tumor or senility.
I understand that you are having trouble getting her in the carrier.
It might help to wrap her in a thick towel or blanket and then pop the whole thing in her carrier so you don't get injured.
You can also use a calming pheromone spray called Feliway. Spray it in her carrier, on the blanket or towel in the carrier and in the room she sleeps in to try to calm her. Try feeding her favorite foods in her carrier so she associates her carrier with a positive rather than as something scary.
In the meantime don't use your hands (or any body part such as feet) to play with her.
Use toys, especially fishing line type toys that she can chase should she want to play.
If she does bite you yell "ouch" and then walk away and ignore her, play over.
If she continues to attack she's likely overstimulated. Use a towel to scoop her up and put her in a quiet "time out" room.
Never try and discipline with your hands. She is already overstimulated and she will just get more excited and bite harder.
Some cats get overstimulated by physical attention/petting.
And when this happens they will bite. They don't mean to hurt you, they are just saying "stop!" the best they can.
If she is biting when you are petting her it is important to read the cues she gives before the bite to avoid it.
It's likely her pupils will dilate (enlarge) or she will become tense or her skin will "crawl". If you see or feel that than stop and you hopefully won't get bit.
I would also keep your petting sessions very short with her.
Best of luck with your girl, please let me know if you have any further questions.