Cutting is unfortunately prevalent among young adults. Many people engage in cutting or in other self-harm behavior because they lack the necessary coping skills that would assist them with difficult life problems and emotions. I believe that this is likely the case in your situation.
You asked whether you are bisexual. That is a complicated question. Some individuals report experiencing a time in their lives in which they are attracted to both males and females but later find that they are only attracted to one or the other. In addition, the fact that you are currently experiencing psychological problems makes determining your sexuality a difficult question to answer. You may have a clearer understanding of your sexuality after you become more emotionally stabilized.
My concern is that in addition to cutting you have suicidal thoughts. Suicidal thoughts are very serious. My recommendation for you is to speak to your parents. You need to let them know that you are struggling. It is also important to inform them about your cutting. If your parents knew about your difficulties, they in all likelihood would seek professional help for you.
You mentioned that you are ashamed of your problems but please don’t be. None of these problems are your fault. Not disclosing your problems means that you will continue to suffer. Many people experience psychological problems. They seek help and they receive the help that they need and want. Please inform your parents immediately and call emergency services or go to the hospital if you feel that you might harm yourself. I wish you the best of luck. Please take care.