Can't Take Calc in High School, should I bother applying for Pre-Med courses?

Pre-med is not a major in and of itself. You can major in anything - biology, engineering, religion, etc. as long as you take the pre-requisites that med school requires. Often schools have pre-professional offices or programs to help you stay on the right track with coursework. So you may need to take calc, but no requirement to do it before college unless the college or your major as a whole requires it. Lots of kids start college with just pre-calc under their belt.