There's not really anyway to tell by looking at you or any part of your body. However, most girls start getting their period during middle school or high school. This is normal and healthy. The doctor will know that.
If it is a gyno appointment they are going to ask you if you have a period and specifically when the last one was.
Here in the United States you do not have to let your parents or anyone go in the exam room with you. There's no law or anything. However, I don't know your parents. Your mom might try to insist on going in with you. You can ask her to stay back in the waiting room. Depending on your family that might upset them. I don't know.
Doctor patient confidentiality laws as they apply to minors vary from state to state. Most doctors will try to protect your privacy. However, as a minor your parents are legally responsible for you, and especially if their insurance is covering the visit....it is likely they can access your medical records. Meaning anything you or the doctor writes down on paper or puts in the computer.
Maybe try talking to your mom about it in private before going? I realize it may be stigmatized, but your mom obviously has a period, or she wouldn't have children. Hopefully, she will kind of understand, and be able to help you through this.