OP i am exactly the same and have had insomnia for a very long time. Like yourself i may drop asleep around say 2am but by 3/4am at best, I’m wide awake again and i cannot get back to sleep. Alot of the time i have to go about my day to day routine on those two hours of sleep. I expect my body to want to sleep at some stage in the day to catch up,but it doesnt. This tends to be a cycle for about 3 days and then at which stage my body just literally shuts itself down at any given time on day 3 as it’s shattered. What I’ve been doing lately which has been a life saver is going on youtube and searching for white noise. I use things such as airplane noises or a fan, but if these noises are too sharp, they have pink noise and brown noise aswell.
Before you keep trying medication which i believe isn’t a fix as you will become reliant on them and if you cant get a hold of any/run out, you’ll be back to square one, try this. When you start to get tired, play this. You’ll see in the comments alot of insomniacs use it with great results