Root canal therapy on a front tooth is the easiest. They can go through the back of the crown the same as if it were a regular tooth, I think. The hole in the crown is then filled in with regular white filling material.
Does your tooth react to heat? Most of the time cold sensitivity will reduce in nature as the tooth itself settles down and dentists don't do much with cold unless it becomes unbearable. Does the tooth react to gentle tapping? If it starts to hurt when you drink hot liquids or it hurts when your dentist does gentle tapping, it may need RCT.
Hopefully your cold sensitive tooth will still settle down and require nothing, though.
It can take some time after a trauma.
Good luck! Let us know how you do.
My best to you,
Also, just to add.. my 2 front teeth were both broke in half after my fall.