Second Wind Fitness Center in Hampstead has an indoor pool. They keep it at 82 degrees, which may be too warm if you are a competitive swimmer. (It's fine for folks with arthritis.)
The Wilmington Family YMCA at 2710 Market Street may be a better option for you. It seems to have a 6 lane pool and 4 lane pool. The Wilmington Athletic Club on 16th Street has an indoor pool. Then, if you join a NC Masters swimming club, you can practice at the UNCW pool. Details here:
http://www.ncmasters.org/sac.html