Do I even have a chance at competitive schools?

Some of your lower cost options would be Wisconsin and Minnesota public universities.

Other than that, be aware that engineering majors can be more competitive for admission than the college generally, so take that into account when assessing reach/match/likely/safety.

Some colleges admit to a first year engineering program, but have a secondary admission process to get into specific majors: http://talk.qa.collegeconfidential.com/engineering-majors/2174743-first-year-engineering-programs-secondary-admission-to-major-criteria.html