With your hangnails, make sure that you are getting enough Vitamin C in your diet. Sometimes, if you are getting a lot of hangnails, lack of C is the problem.
I would also recommend that every night you massage a bit of avocado butter around the cuticle area. That really helps!
When you file your nails, try to get a file which has multiple levels...a very hard emery board area for like greater areas, and medium, then mild for gentle filing. Each week, I have to file my nails down a bit. I use the heavy-duty emery, then I use a very light filer to smooth out the edges. Try to also keep a file with you...like in your purse, backpack, etc. for times when your nails might get those little splits at the ends.
Before finger combing, be sure that your hands are well moisturized and that your nails are smooth, then do the finger combing very gently and slowly. I think being slow helps. Avoid a problem before it starts. And, yes, I agree with the others, be sure your hair is well moisturized, too.
I like to finger comb sometimes even before using my regular wide-toothed comb. And, I certainly finger comb throughout the day...very good method I've found for myself.
Have a great evening,
Jade