Not what you're going to want to hear, but exercise is one of those things that you have to keep doing.
If you can? It's the single most effective treatment for depression we know of. It should also, with time, help improve your sleep.
It also helps to take a whole of body approach to sleep. You can't add a whole heap of caffiene on the one hand, and then hope a bit of extra exercise will cover you (dang! I'm a coffee fan too!!).
Give it time. Also, it really is okay to be having bad dreams. For me? Having had a nasty one last night? I'm always grateful for my brain working through its trauma issues while I'm safely tucked in bed, and I can wake up and remind myself, "That wasn't real". I definitely prefer bad dreams to flashbacks that interfere with my daily function in a big way.
You'll get there. Things will normalise for you. Just give it time, and be gentle with yourself. Anyone promising you an overnight cure isn't being honest.