I think it would be hard to diagnose BP against the background noise of being 15. So, get at least 2 opinions, one of which is by someone who is not profiting by people being bipolar.
If you can talk to your Mom about what is going on and see if you can't get into see a psychiatrist. They should at least hook you up with someone you can talk to about what is going on in your life, and they may start you on some medications that may help. There are therapies like Dialectic Behavioral Therapy that are good for things like cutting. Because your behavior does sound a lot like bipolar disorder but it could also be other things. A psychiatrist can sort that out.
They are pretty sure that bipolar has a genetic basis, so if your Mom has it you are more likely to get it. If I remember correctly it is about a 25% chance of it.
Well if one of your parents has DB then yes it is very likely that you could too. Although the issue of adolescents having Bipolar Disorder is controversial. You should go and see a therapist. BD can be treated with medication, most likely some kind of mood stabilizers and therapy, but left untreated, it can be quite dangerous. If your mood swings do not vary so much each time you may have cyclothymia, a milder version of BD. BD is very hard to diagnose, especially if the patient is in a depressive episode, they may simply be diagnosed as a Major Depressive. So if you decide to visit a therapist, bring along a family member who has witnessed your declines and inclines. Only a professional will be able to diagnose and treat you. If you need to talk, just message me.
Good Luck