Hello hxlcyon, I see this is your first post so welcome to PC!

I hope you find your time here to be of benefit.
It sounds like your body is definitely dependent on caffeine, given the headaches and shaking. Have you thought about slowly tapering yourself down? It might be helpful to keep track of how many energy drinks you have on a daily basis, and what times you generally have them. Once you see your usual routine, you can create a plan to taper off slowly, so the side effects aren't as awful to go through.
I don't think energy drinks are a bad thing necessarily, in moderation. I personally have a 5 hour energy 3 times a week (on work days to help push through), and they are helpful. Some people rely on coffee. The trick is to find a moderate amount that won't affect your health negatively. I wish you all the best.
I also see that you suffer from depression. Have you thought of trying out an anti-depressant to help with your mood instead of relying on energy drinks to get things done? If you don't want to go the med route, you could always try therapy or healthy self-help activities like exercise and healthy eating.