Which tests are useful for ongoing exhaustion (muscle weakness, poor cognitive function, hypersomnia, headaches), once sleep & psych dx are ruled out?

Checkup: At your age I would suspect infections, for example infectious mononucleosis. Other possibilities include underactive thyroid or other glandular abnormalities, anemia or other blood dyscrasias and depression. I would start with a complete checkup and testing with your physician or specialist in internal medicine. Referral to specialists, like a neurologist or psychiatrist may then be recommended