Birth control

Ladies I have not been on any form of birth control for 5-6 years. I’ve only had the pill. It cleared my acne (the reason I took it) but made me depressed and my anxiety through the roof. I hate taking anything hormonal as we have cervical and uterine cancer in the family. I’m 2 months pp and don’t want another baby for 3-4 years so scared to have sex even with as much protection. What do you ladies suggest? My doc gave my the lowest form of hormones a pill can offer but can work the courage up to start taking them.