Is it normal for swelling after an alar rim graft to last more than 3 weeks?

Thank you for your question. 
With any nasal surgery, the name of the game is patience. At one week, we would expect you to have quite a bit of swelling and bruising still noticeable and may have trouble breathing out of one or both nostrils. By the end of two weeks, typically, you will still be swollen but look more like you have a bad cold, rather than post surgical. Swelling can take up to a year to be completely gone, however, by 9 weeks you will look very good and should see big difference from your pre-op pics.

Photos would help, but 3 weeks is too soon to come to any conclusions.  You are still going to have significant swelling at the site, this could contribute to what seems to be an over-correction.  The swelling should start decreasing at this point, but it will be a very slow process.

You bet! I would expect swelling to be present 3 weeks after alar rim graft placement. The size of the graft will influence the duration of the swelling.