A makeover is most commonly when a woman (usually) gets a new hairdo and clothing to drastically change her appearance. The writer is saying thay his sleeping habits are very poor and he needs to make major changes, not just change something small.
A "makeover" is a procedure whereby a person dramatically changes the appearance of his or her face and body through surgery. It is also used to describe a complete remodeling of a home.
The meaning of your sentence is I need to make big and permanent changes to my sleeping habits. The speaker probably gets too little sleep or sleeps at odd hours and feels tired all the time. H