Any suggestions as to what I should do if I want to take the BC exam while taking the AB course? I’m definitely going to be cranking many calc problems as well as maybe getting ahead several chapters in the summer, but I’m unsure what resources to use when I self-study BC. Also, if anyone could provide “harder” chapters of BC it would be helpful when I plan my study schedule 
Why would you take an AP exam in a course you had never taken?
First of all, why would you want to take the BC exam? AB is good enough for virtually all universities (and more than most expect; there are kids who finished with “only” precalculus and went to Harvard). Small story short: don’t do it. It will just be a waste of time and energy. As @bjkmom said, why would you take an AP exam in a class you’ve never taken? Calculus BC is an extension of Calculus AB, so what you learned in Calculus AB is only half the story in the bigger picture. At my school, BC covers all of AB in the first semester, and I know that in other schools, AB is a prerequisite for BC. Also, if you’re thinking about taking BC next year, that’s also not wise because colleges will think that you needed 2 years of calculus AP, when instead you can do AP stats or a higher level DE Math (Calc 3, linear algebra, etc).
I recommend you take the AB exam and do well on it. Why try to learn Calc 2 on your own and jeopardize doing well on AB?