Just keep rubbing a tiny bit of chapstick or Vaseline on his lips several times a day.
Make sure that he is getting lots of fluids also as he could be a bit dehydrated.
The humidifier is a great idea, especially in his room at night.
Last week's cold
& stuffy nose might have forced him to breathe thru his mouth too much.
That has led to his cracked lips.
Hope to have allayed your anxiety