It is normal for new piercings to cause redness of skin in the first month or 2. My sister got a new ear-piercing recently and her ear swell up like crazy, but that was just normal.
If you got received some sort of cleaning/disinfectant fluid when you got the piercing, you can use that to prevent any swelling. If you didn't get that, go to a pharmacy and tell them about the redness around you piercing. Pharmacists are certified to help with minor problems like these and will know what to do/give you.