The is inside Dragon’s Hole , given by a Dragon Tamer after a mandatory post-8th-gym battle. Do not waste hours searching the Ice Cave or Lava Cavern. Simply:

Since you just earned the Dragon Badge from the Iris Town Gym Leader to unlock the area where you found the HM, you should technically be able to use it immediately. However, if you picked it up on a previous save file or through a glitch without the badge, you must go back and defeat the Iris Gym Leader.