Are there any top colleges that don’t require recommendations?

I’m not sure anyone is saying that it makes no difference. But I also don’t think we can assume, just because OP is reserved in class, that she (she? I guess I’m assuming gender based on cheer, which perhaps I shouldn’t…?) is a complete cipher to her teachers. They have read her writing, which may in fact be insightful and impressive; and they could well have observed traits like diligence, reliability, sense of humor, and kindness to others, even if these traits manifest quietly. People are often less invisible than they think they are.

Yes, apply to some no-recommendation schools, but to rule out a whole swath of higher ed just because asking for recs is uncomfortable… that sets a terrible life precedent and makes little sense. Sure, don’t apply to schools that are high reaches and depend upon exceptional recs and EC’s. (Many of those would be unaffordable anyway unless your $45K budget is also your EFC.) But schools where OP is in the upper 50% of applicants stat-wise are worth a try, even if the recs turn out to be a bit more vague than is ideal. Why rule out a school like Clark, where OP is above the median stat-wise, and where just one academic teacher rec (plus the guidance counselor rec - and let’s face it, those folks hardly know anybody) is required? Applying non-binding Early Action will get you a decision before the holidays. You’d need at least 10K of merit to afford Clark, but 65% of students do receive merit aid. And 25% of Clark students participate in their accelerated BA/Masters program, with the one-year Masters program added on for free - an M.A.T. (teaching) is one of the options.

If you think you’d like a women’s college, Simmons could be worth a look - you’d have a decent chance at enough merit to make it affordable, and Boston is an amazing place to be a student.
http://www.simmons.edu/academics/undergraduate-programs/psychology-ba
http://www.simmons.edu/academics/undergraduate-programs/sociology
http://www.simmons.edu/academics/undergraduate-programs/elementary-education-ba-or-bs-mat

Also apply to some no-recommendation-needed schools.

U of Minnesota Morris is a great example of a small (1800 undergrads), personalized school with programs that look like potentially a good fit… yet it has rolling admissions, and recommendations are optional. You could apply when the application opens and probably have an acceptance within weeks, which could be a great stress reliever. (Your stats are right about at their 75th percentile, which means you’re likely to get in, but not so overqualified that you’d feel like an outlier.) And the estimated OOS COA is only $26,392, so it’s a financial safety too. And if you were to feel that you had outgrown the small-LAC environment after a couple of years, transferring to the UMinn Twin Cities flagship campus just requires a straightforward internal application.
https://academics.morris.umn.edu/elementary-education
https://academics.morris.umn.edu/sociology
https://academics.morris.umn.edu/psychology
http://morriscougars.com/sports/2017/6/5/co-ed-cheerleading.aspx

UNC Asheville (3800 undergrads) has only the check-boxes counselor recommendation. Admissions are rolling here too, and a near slam-dunk with your stats. (But you’d still be in the middle of the upper quartile, not off the charts.) Gorgeous location and town. And their program is designed to help undecided students figure out their paths. https://admissions.unca.edu/majors-and-minors OOS COA: $33,248
https://psychology.unca.edu/
https://socanth.unca.edu/welcome-sociology-anthropology
https://education.unca.edu/
https://uncabulldogs.com/news/2018/2/1/unc-asheville-cheer-dance-team.aspx

In your home state, you’d have a decent shot at Pitt’s main campus (your SAT is above median… their median weighted GPA is 4.0 but maybe yours isn’t far off - you didn’t give a weighted number… and the non-STEM majors are less competitive than engineering and premed majors) and maybe you’d like this program https://www.education.pitt.edu/AcademicDepartments/PsychologyinEducation.aspx But it’s a big school with 19K undergrads. Some shy people would like a big, urban school where they can be independent and find their own crowd; others would find it overwhelming. Re: recommendations: “Any and all letters of recommendation are read. We do not require recommendations, but they provide strong support for scholarship candidates and borderline situations.” http://www.part.pitt.edu/faqs.html Pitt is still less than half the size of Penn State, and vibe-wise seems more introvert-friendly than PSU, though folks with direct experience are invited to correct me if my impression is off. There’s an assortment of first-year Living Learning Communities within which to connect with like-minded peers. Upping your SAT to a 1450 (not completely implausible with some prep) would qualify you for Honors, which has its own LLC.

Of course there are lots of possibilities, but… those are some to think about.