As others have said, you definitely need to rework your list. Purdue, VT, UT Austin, and GT all share the attributes of being 1) unaffordable for an OOS low-income student and 2) extra-competitive for CS, when in fact your math/CS scores and EC’s are not the strongest part of your application. OSU could be possible if you could win the Morrill - MSP | Office of Diversity and Inclusion, The Ohio State University - you could be a candidate for this, but it depends how extensive your community service & research work has been. U of Cincinnati (where you’d be eligible for almost-in-state tuition via their reciprocity rate for KY students) also has a large diversity scholarship, among other merit scholarship opportunities Incoming Freshmen Scholarships - About UC | University of Cincinnati and an excellent co-op model CS program.
Are you at least going to apply to Berea? They do have math and CS majors, and it’s guaranteed to be affordable; great alumni network for internship opportunities, etc.
You need to be looking at schools that will meet full need, or come close to meeting full need and fill the gap with merit. If you want math/CS, you don’t necessarily need a college that has engineering; and you’re a stronger applicant for schools where you don’t have to apply specifically as a CS major. There are many good options!
How far from home are you willing to go? It’s understandable if you feel you need to be close enough to get home if something comes up with your mom. I’m sorry to hear about her illness.
Some good suggestions have been made already. In MN, in addition to Carleton, look at St. Olaf, which is a slightly larger LAC in the same town, which also meets full need and has very strong math and CS. Run the Net Price Calculator for St. Olaf - could be a great option if affordable. (FWIW they have a very high Early Decision admit rate.)
Denison (just outside of Columbus, ~35 miles from OSU) meets full need and is particularly committed to diversity. In addition to math and CS, they have an excellent Data Analytics major that might be of interest.
Lafayette and Lehigh, rival LAC’s very close to each other in PA, both have engineering programs and strong CS. Both are trying to increase diversity, and give a significant “bump” to URM applicants.
U of Michigan meets need for low-income OOS students; run the NPC to see whether it looks feasible financially. You can do math/CS in Arts & Sciences - no need to apply to the engineering school.
In the southeast, possible full-need-met reaches include U of Richmond, Wake Forest, Washington & Lee, and U of Miami. Miami has a large diversity scholarship as well, and W&L has the full ride Johnson scholarship. Wake would probably not be in reach unless you applied ED.
Consider Centre College, Rhodes College, Hendrix College, Sewanee, College of Wooster, and maybe Beloit if it’s not too far. None of these meet full need, but all would be reasonably likely to fill the gap with merit and give you a full-need-met offer.
Have you had a paid job during high school, and have you been helping out more at home because of your mom’s illness? Both of these count as EC’s and should be detailed on your applications.