What are the effects of getting a tattoo besides infections? Can a cancer/ heart patient get a tattoo?

Social consideration. Tattoos do not have adverse medical effects, expect in a person with a skin disorder and the infections you mentioned. However, visible tattoos may interfere with the person's ability to get some jobs. It is an individual choice, but tattoos are a form of self mutilation.
Regrets. You're only nineteen and are being treated for anxiety. Both are great reasons not to be inked right now. I'm a tattoo buff and have two of my own. Wait a few years before you decide on what you want and when you get it. "No tattoos before 30" is a good rule unless it's your military unit's tattoo, and no names of anyone who's still alive are also good rules. Most anyone can get inked.