A Rebbe of mine once told me that "your day starts the night before". And he explained that this is a big trick of the Yetzer Hara to make us stay up late at night and not get enough sleep. He even tricks us into becoming "temporary Tzaddikim" by giving us an inspiration to LEARN late, cuz he knows we're gonna miss davening in the morning AND forget the learning anyway, since we were tired when we studied it.
My prescription? Try this for 3 days: Don't eat after 8 pm, but water is OK. Absolutely no video stimulation for the 2 hours before bed. Turn off the phone. Set up some quiet instrumental background music, or get one of those cheep sound machines that makes pastoral or rain sounds for noise. At the same time, curl up IN BED with a nice "Visions of Greatness" book, or something with SHORT inspirational stories (and read the happy ones, not the Holocaust ones). Limit yourself to 20 minutes of reading AFTER you take one of the following sleep aids: Sip a nice cup of Wisskotsky's Sweet Lullaby Tea (it's decaf). Or, if you're the type, (and nobody yell at me, this is only for temporary use), take some over the counter melatonin or Sleep MD (all natural sleep aids). Of course check with your doctor first, and also to know how much to take. Do NOT take too much, even if the box says it's not habit forming. BUT GO TO BED THE FIRST NIGHT WITH 10-12 HOURS available before you have to get up. At least 9 hours. Cancel a chavrusa if you have to - this is an investment in your future.
Do this for 3 nights in a row. No excuses. See what happens. You need to reset your internal clock. And you need a safe and healthy way to get you to sleep long enough to experience REM sleep and proper dreaming.
If you're still exhausted, even after being asleep for 8 hours for three days in a row, then please consider getting a sleep-study to test for sleep apnea. Many people have this without even realizing it.