The best piece of this post is hidden in a sentence in the middle, and I wanted to call it out:
If cost is an issue, go to a community college BEFORE going to a 4-year engineering school. Community colleges are a fraction of the price of a university.
Any EE degree is going to require a significant investment in calculus, some diff eq, linear algebra, chemistry, physics, and likely some humanities.
With some clever coursework you can do ~2 years of full time EE coursework at a community college.