I am studying ap calculus now, before I move onto differential equations etc., but the thing I am unsure of is, should I learn set theory before continuing on my ap calculus sections?
Short answer: No.
If you really want to know a little bit about sets, the first section of Book of Proof or Applied Discrete Structures would more than suffice for the purposes of most collegiate level courses. (You'll want more of them for courses involving proof, of course, but no more set theory.) Especially the first is quite suitable for self study.
But while there are some basic calculus arguments (especially once you start looking at vectors and/or parametric things) which can involve sets a bit, if you are studying on your own, no need to complicate matters by studying them separately. Whatever calculus text/resource you are using should have enough background to make progress - and if it doesn't, find another one. This website has several English-language open access texts, one of which should suffice for your needs.