It is normal for the site of the tattoo to have a little swelling, due to skin irritation, immediately after the procedure. This may last up to 48 hours. However, anytime the skin is broken - whether due to a prick, incision or cut - there is always a potential for infection.
Skin infections can be caused by using unsterilized equipment or lack of sterile conditions in the tattoo setting. They can also be caused by the artist's poor personal hygiene (not washing hands or not wearing a fresh pair of gloves after each procedure) or by the client not diligently following aftercare instructions.
If the condition of the skin seems to be getting worse, not improving, or developing new symptoms such as increasing redness/irritation, swelling, pain, discharge, odor, fever, red streaks, or sores on or around the tattoo, you should seek medical attention immediately. The rule of thumb is, if you ever feel something is not healing properly or something does not feel right, seek help. It is always good to be on the safe side.