So it’s late in the game. You are in KY but would you consider the Northeast?
Some good/affordable options
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TCNJ is $40k total (tuition+R&B) for out of state. They are considered the NJ state honors college, they have STEM majors including BME, and they even have a medical program so the pre-med path is well established. The campus is near Princeton.
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SUNY Geneseo - the small SUNY schools are even cheaper. For example, Geneseo is 35k total. This is the small LAC honors college for the SUNY system. It’s very rural and in the middle of the state between Rochester and Buffalo. There are a bunch of other smaller SUNY LACs like Oneonta.
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SUNY has four large, well-regarded flagship campuses with strong STEM Programs. these are more expensive. U of Buffalo is the engineering college. U of Albany and Stony Brook are the update and downstate medical centers. SUNY Binghamton is fairly competitive for admissions and it might be too late. Not sure.