I'm unsure why you dissed your Ts idea of a routine by saying you've always had sleep issues. To me that means you have always needed a routine.
A good sleep routine is a good way to help solve this issue. You might also have sleep apnea which could be the reason for being in bed "sleeping" all night and waking tired...you are tossing and turning and not breathing well and constantly waking without knowing it..just to breathe? But a good routine is cheapest and best to begin with anyway.
What makes a good sleep routine? You go to bed and get out of bed every day at the "same" time. I would say within 30 minutes of the stated desired time.
Shut off ALL electronics at least an hour before bedtime. Some people need to make this an hour and half to two hours before, depending upon the brain activity and the types of media they watch/listen to. This includes TV, smart phone, iPad, computers (in any form), radio, regular phone etc. everything. There is something about the activation of the brain and lack of sleep...
Then you need to look at what you are eating and drinking and when you are eating and drinking. If the body needs to be digesting a big meal, well, you aren't going to sleep well. If you've cranked your system with diet sodas and sugar, likewise it won't function well when you want sleep.
Make a list of things you need to accomplish/finish the next day. Keep a notebook by your bed and if you wake and think of something, write it down and go back to sleep. This prevents the brain from keeping it in your conscious state so as not to forget it. Then... if the thought arises tell yourself, I wrote that down, I'll work on that tomorrow, it's nighttime and nothing can be done about it right now...
Then give yourself good thoughts... positive affirmations... pray... meditate... read a good but not exhilarating book... for 10 - 20 minutes... to help the brain calm and to clear your active mind and ready for sleep.
You can try delta wave brain CDs or hypnosis scripts being read to finish the routine if you like.
Your bedroom should be as dark and quiet and cool as you can make it comfortably. I personally even have stickies over the alarm panel and smoke detector lights, and a cover over the cable modem lights. You'd be surprised as to how much light these give off in the dark, and they do affect the brain.... See how much you need to cover by beginning with all of them covered... everything shut down (including a noisy clock!)...
You can also try "white noise"...or forest sounds or rain showers... in the background to help lull you to sleep.... but not music that you might begin singing to etc.
There are many other ways to develop a sleep program/routine. Your T can help you.