Did you get your green card yet? I don’t think cost will be a “minor” issue if colleges still consider you an international student.
What does this mean? College financial aid offices base their offers on the financial info. you provide. If they decide you’re in the international pool, the aid you get will depend on what they offer international students. If they consider you a domestic student, they’ll base aid on formulas using FAFSA and/or the CSS profile. Have you received your financial aid packages yet?