OP, look at less selective schools for engineering, for sure. There are some that will take you if you have 3-4 years of math, physics in senior year, good gpa, and good test scores.
My son was weak to be an engineering applicant, but applied to some schools in engineering anyways. However, he was stronger than you and had a strong SAT score. He applied to about 6-7 majors, and ultimately, did not have an interest in engineering. Here are his engineering results, fyi:
SAT: 2230
SAT II Math 730, Physics 610
GPA u/w: 3.84
Community college classes related to engineering
Junior year courses: Trig (fall), Intro to engineering (fall), General Physics (algebra/trig based) (spring)
Senior year courses: Pre-calculus (fall), Calculus I (spring)
Univ. of Alabama, Huntsville (great school and good scholarships)-admitted for Mechanical Engineering and honors program
Stanford-Denied for Product Design (engineering degree)
San Diego State University-Admitted for Mechanical Engineering
UCLA-Waitlisted for Electrical Engineering
Cal Poly SLO-Waitlisted for Mechanical Engineering
Missouri S&T-Admitted for Metallurgical Engineering
South Dakota School of S&T-Admitted for Metallurgical Engineering
He was not a strong engineering applicant. He was admitted to the schools that have high admit rates, and waitlisted or denied at the selective schools except for San Diego State.
As long as you are shooting for schools that have an admit rate above 60%, you may have a shot at an engineering school. Anything more selective, and I honestly don’t think you have the background.