How long will it take for the swelling after scar revision surgery to go away?

Postoperative swelling is usually normal, but it is important to talk to your surgeon to make sure the swelling is not due to a hematoma or infection. If it isn't, then the swelling should subside in a few weeks. 

Although each individual heals at a different rate, the steadfast rule of thumb for duration of most of post operative swelling is generally 6 weeks.   After the 1st 3 days or so ice will not help the swelling anymore.

A week is very early in the wound healing process. It is normal to have some sort of edema for a week or two, then the actual tissue is bumpy for a few weeks after that. usually around the 6 week mark, the redness is improved and the texture begins to flatten out. I would give it time and ice at this point will not help. Best of luck