What are these tiny pimple-like white spots that grow under my scars?

What you describe fits with milia. Not sure why you think it's not that. They can form in acne prone areas, but also at sites of injury, even the palm. Simpl breaking the skin over them and pushing them out ot pulling them out is most effective. Things like retin a may be used for those in acne prone areas, but it's not good for healing wounds. They occur when the skin heals and crosses up the glands and skin gets trapped beneath the overlying skin.