Are you sure you have insomnia?
Most people who think they have insomnia actually have other sleep issues.
I have had medically recognized insomnia twice including hospitalization... once as a side effect of medication and once as a side effect of sepsis.
The thing most people dont understand about real insomnia is you don't really feel or get tired, it's like being constantly wired and hyper 24 hours a day.
With the sepsis I went 5 days unable to sleep (my body kept trying to sleep but the startle reflex kept it from happing) but never felt tired at any point and I ended up needing sedation.
The medication included a stimulant that stopped me being able to falling asleep and kept me feeling like I was on redbull, we had to adjust stop the medication in the evening and night to give it time to wear off so I could sleep.
I use to think I had insomnia before then this but it just turns out I'm a very light sleeper, a 'night owl' and have a very active imagination which stopped me from falling asleep 'on schedule' which lead to me being constantly tired but that is not remotely the same as the two times I had insomnia.
Other conditions like restless leg or apnea etc... can also cause an inability to fall asleep and lead to severe tiredness, if that's the case figuring out the cause could help you figure seek out a cure.