Thanks for sharing your concern.
The cut in your gum suggest two things.
one is that your brush is too hard.For this you need to replace your tooth brush with a medium/soft bristle bush ,based upon the texture of your gums.
second and most important thing is that, the manual dexterity with which you brush.
you have to brush your teeth gently with focusing on it ,also you do not have to spend more time brushing it.just 7 to 8 strokes is enough,followed by through mouth rinsing.
If it is possible for you, then you can go through various brushing techniques,learn them and brush your teeth effectively.
can also help you in this regard.
meanwhile apply DOLOGEL or Mucopain oral ointment over the affected area .
Hope it helps.