What does mending bone feel like?

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There is no particular sensation associated with bone healing.

Because the trauma which caused the fracture likely caused other damage to soft tissues including nerves, it is not uncommon to experience paresthesias. But tingling could also indicate undue pressure on a nerve or swelling causing such pressure. Tell you doctor and let him/her decide.

Yes

Possibly . . and some fractures are less prone to heal well than others.

Not likely if the fracture segments are adequately stabilized and immobilized. But, as you are experiencing pain, perhaps they aren't.