Only a doctor/psychiatrist can diagnose you with bipolar disorder or not. But you can research the topic, arm yourself with knowledge, and be ready for your appointment.

Being bipolar means you have two extremes. The up (manic) and the down (depressed) extreme. You sound like you have the down, due to your emotional crying. Your up needs more information, such as a doctor would ask you. Trust me, you don't WANT to have bipolar, it is much easier to have depression or OCD though both have their bad side also.

Read some more articles on the topic, and slowly convince your mom to seek some sort of medical help. The next time you see your doctor you can tell them also, he can help you with this process.

Let me ask, when you are sad do you ever think about hurting yourself?

If that is a yes, then you can also seek help at school. When you are having a bad down day go seek out your school counselor, they will help you and that can help you get your mom to believe you.