Yeah bipolar disorder is what I was kinda wondering (I was recently diagnosed and frequently find myself on a huge crusade to prevent people going through what I went through. *shrugs*). Anyway, it's good that your up times don't cause a problem, rules out that one which is definately good.
The thing with psychologists is, whilst they may have an idea what's going on with you, they can't diagnose you, and can get it wrong. I speak from experience. So I think you really need to see a doctor.
Fair enough, you're uncomfortable about seeing your family doctor- but you do realise if he/she were to mention anything to your parents he/she would be in big trouble? If you're not comfortable, what about asking to see another doctor at the practice, or trying somewhere else? There is really nothing to stop you seeing a different doctor, and I think you need to. Look, if you're still feeling like this, the talk therapy ain't working- you may well need a different type or anti depressants. I can't say, but it's worth looking into.
Finally, suicide isn't something you 'grow out of'. It's not a question of growing up and learning to deal with your problems. Feeling suicidal is a huge warning sign something's wrong. It's not normal to want to die, and it's not something you can shake off without help. Depression is an illness. Please, please get yourself some help, because it does sound like this could be your problem.
Really hope you get some help and start feeling better soon.