How to come off birth control without loosing hair

Hi! I am 41 years old and feel birth control is a contributing factor to my rapid hair loss. I am currently on my first month of the NuvaRing. I am not sexually active at this point in my life but have stayed on it for acne purposes. I am willing to come off in order to stop the rapid hair loss but read that coming off could make it worse.

This is my first post. Could someone direct me to a thread on this question: How to come off the pill properly as to reduce hair loss?

Thank you!