The lack of sleep is a side effect of the stress you have going on in your life and the anxiety from that stress is effecting your hormone levels which effects your serotonin levels which is why you get insomnia.

Since your in college/high school (I don't know) you can ask your teacher right now to take an Incomplete. That will mean you are given an "I" grade and your assignment deadlines will be extended. If your teacher refuses to give you an Incomplete, ask your registrar to give you a "W" or Withdraw grade from your current course/s. Having one "W" on your transcript isn't the end of the world. Or, ask for a Medical Leave. It will still appear as a "W" but for medical reasons. Talk to your registrar about your options.

If you think you can finish your assignments, try do to that. But if you know you are too overwhelmed right now, then you need to take a semester off.