That is weird, I have the exact same problem. Just that it has been going on for a few months. It became a little better in the middle but now I am back to the same problem. My eyes are burning,so tired but I cannot sleep. And even when I sleep it is not the deep sleep I used to have.
For me atleast it started like 5-6 months ago with VIVID dreams and then around 2-3 months ago the lack of sleep started. It started with an anxiety attack about a health scare.
Went to the doc, got some anti anxiety meds, got some tests done. Nothing looks wrong according to the doc. The meds made me drowsy constantly but did it for 2 weeks. Slight improvement. And now it feels like I am back to square 1