A person who's careworn is so tired that it shows on her face. New parents who have been up all night with a crying baby often appear careworn.
Nights of interrupted sleep, working a late shift, and traveling a long distance can all make you a bit careworn. Simply fretting or worrying about something is another way for your expression to be careworn. The word emerged in the 19th century, from care, with its Old English root caru, "sorrow or anxiety," and worn, from its sense of worn out, or exhausted.