I don’t know if you have depression. I do know you have plenty of reasons to be sad and angry. Everyone in your family is in deep distress. It doesn’t surprise me that you meet the criteria for cyclothymia, but I do caution you that the situation may be causing you to look mentally ill when really you are upset about things that are very upsetting.
The best thing your family could do is to go into family therapy together. You would not have written to us if you were not concerned about your parents and sister. They and you are all reacting to each other which is an indication of how much everyone cares. With some family treatment, that involvement with pain and hopelessness can be turned around so that everyone could instead support and encourage each other.
Ask your doctor for names of therapists who can help. Then follow through. Even though you are only 15, you could make the phone call to the therapist to see about availability and cost. You can then take that information to your parents and ask (plead) that they make an appointment.
I wish you well.