You're fine. Schools will see your GPA and grades for individual classes. They may ask you about specific grades during your interview or they may not. Its not a big deal. Just be able to answer why without any excuses and what you learned from it/how you took steps to prevent it from happening in again. FWIW I had ~15 Cs on my transcript (I only retook 3 of them), a D, and 3 Ws. The only one that was brought up during interviews was the C I got in Skills for Academic success (a BS class required your first semester). I flat-out said I was immature and didn't invest myself because I didn't care, then went on to discuss how I matured, took accountability, and turned my academics around. The interviewers nodded their heads, wrote some stuff down, and the interview went on.
Edit - Just checked the exact number was 16 Cs. 6 were in pre-reqs (Bio I, Ochem I&II, Ochem Lab I&II, and Biochem I), 3 of which I retook and got As the second time around (Ochem I&II and Ochem Lab I).