For starters, your scheduling snafu isn't “grave." Save that designation for the day that you sign up for Woodshop I and land in a classroom with 37 freshman boys using power tools. 😉
Similarly, skipping out on calculus won't “make or break an application." That's a bit extreme as well. But, on the other hand, you're correct when you note that successful candidates at Wesleyan and at other “elite" liberal arts colleges and universities have commonly taken math through calculus. While you won't automatically put yourself on the cement deck of the applicant pool without it, you will, in fact, be at a small disadvantage, even if your intended major is in the humanities.
So, as you've suggested yourself, it might be wise to study on your own over the summer to get ready for calculus next fall, although—if your high school offers regular college-prep calc—you need not aim for AP, if you feel that it's too big a leap after self-studying. Better yet, take an actual summer class. Community colleges typically offer at least a couple summer sessions between late May and August, with classes often held at night as well as during the day. If you live near a four-year university, you may find a summer session there, too. There are also many on-campus residential programs aimed at high school students that include math courses. These programs are usually lot pricier than those at your local public colleges but would provide the opportunity to concurrently take other classes that may interest you more while you test-drive dormitory life and engage in fun activities and excursions with peers.
Bottom line: You haven't torpedoed your college process by straying from the accelerated math path, but if you can hop back on that path this summer, you'd probably be giving your admission odds at your top-choice colleges at least a small boost.