My son (now 12) has hated hair cuts since he was a baby. As a toddler, I would hug him as he got his hair cut and he would just cry and cry. As he got older, we could no longer go to barbershops or even specialized hair salons. He started hitting the stylist and eventually wouldn't go in. One day, I got the idea to cut his hair while he was showering and he resisted at first, but now that is the only way he will let us cut his hair. My husband has to "catch" the falling hair in the garbage can as I cut as quickly as I can.
As for hair combing, that used to be a problem too. We actually went to some therapist who started playing the "where is my hairbrush" song and then doing (Phone number can only be seen by the question and answer creators) as they got him to comb his hair. he would only comb it 10 times for the longest time, but now, he is better and will even comb it himself.
I don't know if either of these methods would help you, but it's worth a try!

Yikes. Can relate. I hated having my hair done when I was younger- super sensitive to the brush. Even today I can’t use certain hair ties etc. I understood what E was going through so most of the days, when she was younger we used dry shampoo that made hair soft and just ran my fingers through it to make it presentable. As she grew older, 6 ish, I gave her the choice of doing her own hair- worked! Now she just does her hair several times a day. Had to try various brushes to find the ‘right’ one. Don’t get her haircuts if she doesn’t want to. That person hasn’t earned her trust. We worked on finding the’right’ person and again it was a breeze. Once her regular person wasn’t there and she almost bit the hairdresser. Don’t blame E though, that hairdresser was insensitive and impatient and we left without a haircut. One she said she didn’t want to be some place we left. Anyway, now E can have anyone cut her hair because of the positive experience with her favorite person.

Have a comb out at all times. Every chance you get try to let her pick up the comb and play with it. Even you can have a comb out and slowly brush your own hair in front of her. If you make it a routine habit she might open up to it more and pick it up on her own and make it easier.
I had the same problem with my boys getting their haircut. I had to get an app on my phone to simulate the noise and I would have my phone vibrate and rub it against their head. I would do this everyday for two weeks before they get a haircut.