J.S.
We definitely had this problem in our house! I have found with my sons that their noses were just dry. At the suggestion of my pediatrician I've been swabbing the inside of their noses with Vaseline or Aquaphor Ointment. My eldest, who is 3.5 years old, now he tells me when his nose is bothering him and he asks me for his nose medicine! Good luck. I hope you find something that works for you.