That's really debilitating, lack of sleep. I use a relaxation app and go swimming, which helps but like you say if you're so exhausted from lack of sleep you can't do the things you need. I think our bodies get into a bad habit and it takes a while to break it.
Presumably you've cut out caffeine and other stimulants? A friend of mine swears by eating salad in the evenings as there's supposed to be a chemical in lettuce leaves that helps you go to sleep.
I hope you sort this soon. In the meantime have you tried getting out of bed when you can't sleep and doing something else? So your body just associates bed with sleep and not lying there wide awake. try reading or even writing down how you feel, that always helps me.