First gynecologist visit help?

Ok so I’m 16 years old, almost 17. I’ve been sexually active (sex once a month) for about 9 months now. The past few months my cycle lengths have been increasing, almost at 50 days.

I told my mom I want to get on birth control to straighten it out, so she’s gonna take me to the gynecologist to see what they suggest.

When I go to the gynecologist, I will have not have had sex for well over a month, and I ended my period about a week ago. Therefore, obviously I’m not pregnant. So if I tell the gynecologist this even though I’m sexually active, will they still take a pregnancy test?

If they take a pregnancy test or give me a Pap smear, will they be written out on the bill for my mom to see? I don’t want her to know I have had sex even though we waited a long time to lose our virginities and we’re the closest people to each other. I’m scared and don’t know what to do, please help. :(