Can tattoos get infected?
Not as long as you take care of your new tat. There is a section in the FAQ that covers healing methods in depth.
Some people have trouble healing tattoos with colors they are allergic to. If it gets infected and refuses to heal after a few days of using a topical antibiotic, you may want to check with a doctor.
Keep in mind
This assumes you are a healthy individual without any condition that suppresses your immune system.