so let say i have 2 facedown damage point to my round previous turn, this turn, i get a damage and damage card says, turn one of the damage card face up, so i turn one of the them face up, does the card that turned face up this way apply its effect?

When an investigator claims a Damage or Horror with the
Resolve Immediately trait or flips one faceup, he immediately
resolves the effects of that card, which typically includes
flipping the card facedown.

Page 7 of rules reference under Damage & Horror