Will a sudden change in career path affect my application?

I’m in the Class of 2018. Basically, here’s the issue. For most of my high school career, my classes and some of my extracurriculars have been centered around the idea that I’m going to be a biology major, do pre-med, eventually become a neurosurgeon. But a few months ago, I discovered that I’d rather be a psychiatrist, and that a psychology major fits my interests better. But since I’m a senior now, I don’t have a single peer counseling class on my transcript & I don’t have enough time left to become a counselor, and I am taking a psychology class for the first time this year.

Will applying as a psychology major with little psychology background hurt my application?

no.
If you really want to become a psychiatrist [ which means you have to be accepted to med school first, then do a residency in psychiatry] then you will have to take basic premed science classes in college, and do really well in them, and if you have time, you can take psychology classes as well.
You will have plenty of time to decide what really interests you in college, so dont try to decide now, or worry that colleges take students based on their career goals- most dont even ask what your eventual major might be.

This won’t be a problem at all. A LOT of students change their major even after they get to university. Changing your intended major while still in high school is very, very common, and will not be a concern for any university admissions people.

As @menloparkmom said, if you want to be a psychiatrist then you have to go to medical school first. If you want to be a psychologist, that is a somewhat different path (although close enough that you will not need to decide between the two for a few more years).