I am so scared about the general anesthesia part
it's normal to scared of anesthesia, especially if you're thinking of having elective or cosmetic surgery. Most of the anesthetics used today leave your bloodstream rapidly. That's why outpatient surgery has become so popular. Unless you have some major medical problems the risks of anything bad happening are less than driving a car, something I suspect you do do several times a day. Speak to your surgeon about it. You might also be able to speak to the anesthetist about your fears. Make sure that the facility is properly accredited. Good luck.
It is completely normal to be uneasy about having surgery and being asleep under general anesthesia. General anesthesia is very safe when it is performed by a board certified anesthesiologist at an accredited hospital or surgery center. In terms of waking up after a procedure, the anesthesiologist titrates the amount of medication you are given so that it wears off gradually and its wearing off coincides with the end of the surgery. I would suggest that you discuss your concerns with your surgeon and with your anesthesiologist.