Hi.
I'm sorry you've been feeling so down in the dumps. It is true that teens sometimes feel lonely and alienated. This is a time when there are tremendous pressures from many directions--school, parents and even friends. But the fact that this low mood has lasted for a long period of time and that it's affecting your sleep and your ability to enjoy normal activities--like hanging out with friends--is certainly cause for concern.
If you haven't been able to persuade your mother to allow you to see a mental health provider who can do a thorough evaluation and discuss treatment options with you, try speaking with a school counselor. He or she may be able to talk to your mother about the seriousness of the situation and will probably be able provide referrals to a mental health practitioner.
For immediate help, you may also want to look into teen crisis hotlines or depression support hotlines. While these hotlines will not be able to provide a diagnosis or a treatment plan, speaking to someone may help ease the pain you are feeling. One such hotline, called The National Suicide Prevention Lifeline, is available 24 hours a day, 7 days a week. The phone number is: 1-800-273-TALK. You can call them just to talk or to get more information about mental health care.
gURL's psychology resource page may also provide you with other alternatives for dealing with your depression. Good luck and I hope that you will be able to get the help you need.
Best.
