Can my boss tell me to cancel a doctor's appointment?

Unless you have a written employment contract with your company, you hold your job "at will," which means that the law allows them to fire you without any reason at all.  So you're going to have to decide whether the risk to your health, of missing this appointment, worries you more than the risk of losing your job over this (and just how much of a risk we're talking about, in both cases, is mostly something you have to figure out).

Without more facts, it's very hard to say if you are protected by the Americans With Disabilities Act ("ADA"), which makes it illegal for a company to discriminate against employees because of their health issues, as long as they can still do their job, and even requires a "reasonable accommodation" from employers, to employees, making relatively minor changes to working conditions to make it easier for the "disabled" employee to cope.  The ADA covers a very wide range of people, not just those who are in wheelchairs or who have other drastic physical limitation, and it also covers people who have been treated or are being treated for mental illness.