I agree with this. Even if you are on your mother's insurance, it might be that she's unable to see details of your visits. I'm on my husband's insurance, and there's some information that's visible only to me, like if he goes to the account online. And paper statements about my care are addressed just to me. The thing is, a psychiatrist is a medical doctor, and you're treating a medical condition. You could tell them you're going to the doctor and it's personal, or something like that. Though maybe they'd still pry.

Once you do have a job, maybe you could go to appointments during or just before/after work so that they wouldn't know you were going out someplace.

Also, do you have a primary care doctor? If so, this is not ideal, but maybe you could ask him/her if they could try prescribing something for depression? Same with a gynecologist, you could ask. I say not ideal because they won't have the expertise that a psychiatrist would, but maybe it would be something to get you started. And I see you're in the US--some mediation that's available in generic form, you can get at certain pharmacies for like $4, no insurance involved, so it wouldn't show up on insurance.