I was in your same boat. I agree that you need a doctor who will help you look at boosting your energy and sleep with vitamins and minerals. Use the over the counter and prescriptions as a last resort. Some vitamins that helped me were B12 and also lots of Niacin.
Some other safe things you can do that won't affect your breastmilk are chamomile tea or passionflower tea, sipping the hour or so before bed. You also may consider taking Melatonin, which normalizes your circadian rhythm--I'm pretty sure your doctor would agree this is safe, but please ask. The most effective form of Melatonin is sub-lingual, the kind that melts under your tongue as a lozenge. It won't make you sleepy, it just helps you rest when you're ready to lay down, and then helps you stay asleep. People use it for jet lag but it helped me at times when I had several nights in a row like what you're describing. Just so you know, I nursed too.
I also find great relief when my mind wakes up in the middle of the night to check the babe and won't "shut down" with Dr. Bach's Nighttime Rescue Remedy. This is a flower-essence formula that is vibrational medicine that affects your energy body, not your breastmilk. Your doctor won't know much about that or be able to advise you, since it's not western medicine, but perhaps a Naturopathic doctor would, or a certified flower essences practitioner. You can also ask a Naturopathic Doctor (ND) about using skullcap, an herbal sedative.
Best of luck, I've been there, and it will get better. Your body needs nourishment. It's good you're trying to get more sleep because that's probably one of the best ways to avoid illness and depression.