I am considering art school in the future when I graduate but I don't know if I can without having art classes.

I tried talking with my mom on how I wanted to be a graphic designer or some form of a art career and although she didn't discourage me from it, she told me she recommended it to be a hobby and focus on my current path in biology.

Although I like the study or the human eye or of sexuality/gender/sex in general, I much prefer taking an art career. It feels it's the thing I can own and can say it's my art even if I'm free-handing most of the time, but am starting to learn figure/gesture sketching.

I still have a LONG way to go as a artist that I can't comprehend right now, but I haven't even taken art classes in my school and I'm entering into my junior year after summer. It seems I can't fit in a art class until my senior year where I can only take the basic art classes. Junior year filled in the gap of my final year of chinese and my project lead the way courses which I need to stay into till senior year.

I'm looking at the Art Institute in Chicago which seems big. I will look of other colleges if I don't get in but will I able to get into a art school even with only one or two classes of art? Can I still make it if I intern or take a outside class out of my school b/c the art class in my school isn't all that great for me?

It's great that you are getting into art!
If you can't get into any art classes, draw in your free time, try out new techniques and things that are challenging to draw, after a little practice you'll be able to draw really good! Whilst drawing start to get a portfolio of all of your good drawings and if you can't get into any art classes, show said portfolio to the place you are going to apply for, hopefully they will like your work and see your potential!
Hope I helped a bit! :D