Does subcision leave a permanent mark in the spot where facial skin is pierced by the needle to get under the skin? (Photo)

I had Long Pulse treatment to eradicate vein on my nose but the doctor and her team didn't provide enough cooling and now I have depressed scar on my nose resulting from the treatment. I'm thinking of doing subcision to elevate the depressed scar but I'm not sure if that's the right procedure to take. I'm wondering what procedure is best for me and will subcision leave additional scar in the spot where the needle penetrates my skin?