All of the piercings that I have had all were red for several weeks after the piercing. Use a combination of salt and water on it, applying with a Q-tip to help with healing. Don't use alcohol! I have heard it slows the healing process.
The signs of infection are: redness at the site, heat at the site, drainage, and inflammation. If your piercing is very very tender, hot, and draining a yellow fluid, it may be infected. Otherwise, redness is to be expected. :)