If I were to get a C in a class on my transcript, will it hurt my chances of getting into a college?
It depends on the college. It depends on the class. It depends on the rest of your application. It can hurt you at the very top colleges, where they have far more highly qualified applicants than they can accept. But at most colleges one C isn’t going to make a difference.
There is a small handful of colleges where a C might matter. There’s a huge number of colleges that will overlook a C if everything else is good. And plenty of great colleges will overlook two C’s. Apply to a range of schools and be sure you have several that you are sure you will get into.
Don’t get a C and then the question becomes moot.
The class in question is an AP class
So it is a core academic class. That is a bit more damaging than a C in a foreign language (colleges seem every so slightly more forgiving of that) or a class like gym or art or something. Bottom line. Everyone should start with making a list of safeties and matches for their stats when forming a college list. Then add a few reaches. A C in an AP class isn’t going to be helpful at the very tippy top schools.
I’m really not sure what you want us to tell you. Even without the C, your chances of getting into the very top schools are very low (many take fewer than 1 in 10 of their applicants, and some are down around 1 in 20). So what can you, but do the best you can, formulate a reasonable list of schools of varying degrees of selectivity (hopefully that are affordable for your family and solid in your major), and put in your applications. We tell parents to “love the kid on the couch” sometimes. Maybe we don’t say it often enough to the students themselves - you are enough even with some lower grades on your transcripts. You can still get a great college education and go on to the career you are targeting, regardless. Don’t be so worried about a few schools.
Assumes facts not in evidence. The OP said it was an AP class; AP Art History and AP Music Theory are not core classes in general, although how a college chooses to view those grades will depend on the college. I agree with the rest of @intparent 's statement, though.
Ah, that is true. Thank you. 
I mean I was thinking of schools like Western Michigan University, Ferris State University, Saginaw Valley State University, Eastern Michigan University, etc… Not schools like Harvard or Yale
People flunk classes, go to summer school to recover the credit and still get into college, even competitive colleges.
I think you will be okay for those schools. The year is only half over. Just keep doing your best. Are you on a block schedule?
No I have 7 classes per day @Groundwork2022