Congratulations 
that’s an impressive record.
Is the 15-20k budget based on being a middle income family (75-125k for instance) or is it a set budget hoping for merit while you don’t qualify for much or any financial aid?
Fordham only makes ~ budget if your child is a NMSF and s/he gets a full tuition scholarship.
As posters have mentioned, alas, the public universities on your list won’t come within budget. Your child will likely get in but the bill would be in the 40-60k range everywhere.
If you have a low SAI, many “meet need” private colleges will be interested and affordable.
https://www.mefa.org/student-aid-index-sai-calculator#efc
However, if you need merit to cover full tuition or maybe even more, you can look into some universities already listed
Or for instance
https://www.sc.edu/study/colleges_schools/honors_college/about/index.php
If that budget is a bit flexible, look into universities that may have a Flagship match (you don’t pay more tuition than for the flagship) Oglethorpe in Atlanta, Hendrix near Little Rock… you can also see if UMaine’s deal applies to Florida. It’d still cost more than 15-20k though.