Welcome to YT. Tugging on hair mats can be very painful for a dog and tugging too hard can damage the hair follicle and skin.
You have a big challenge if your pup is biting. However, if the mats accumulate on the dog, the mats will pull skin when the dog moves. Hang in there and keep working with your pup, getting her accustomed to you handling her. Take your time, move slowly, and encourage her with a soothing voice and treats. (My boys know that after grooming they get to go on a big walk -- their favorite thing in the world
).
If possible, use fingers first to pull apart tangles. Then carefully work with a comb. Try putting a little cornstarch on the mat to give the hair more "slip." Don't get the cornstarch wet.
Another option is to put a little conditioner in a small spray bottle and then fill the remainder with warm water. Spray on a good brush and then carefully work through sections of the coat. I have had a lot of success with BioGroom Silk Creme conditioner and this brush:
Amazon.com: Isinis Hair Brush * Made In France:...
Some mats are so bad that they will have to be cut out carefully with scissors. Don't try shaving off mats with an electric clipper.
Good luck!