Is it possible to put on your college app that you want to major in psychology but you didn’t take a psychology class in high school? What are the typical classes you should take in high school to major in psychology? Is it hard to switch from a humanities major to a social science major?
Yes.
Usually “social sciences” is a subset of “humanities.” The difficulty of switching majors in general depends on if you have to switch schools/departments, your year in college, how many course requirements you have, etc.
To major in psychology, you’d need good grades in Humanities and social sciences as well as in biology (AP bio can help). A class in statistics may help but even if you have AP stats, take at least one stats class in college (preferably more).
It’s typically easy to switch from psychology to sociology, economics, English, etc. However it’s almost impossible to switch to engineering from psychology. 
My kid wants to do the same. You can major in anything you want to in college. Unless you go to a college that specifically teaches engineering, etc… Just get yourself into college first, and when you do, the guidance center will put you on the right track.
It is fine. In general colleges don’t pay a ton of attention to an applicant’s intended major. At most colleges majors are not formally declared until the second semester of sophomore year. It is well understood that many students apply undecided and many others change majors once they get into college.