No, medical school is a whole different ballgame. The AMA limits the number of medical students per year and tightly controls the system.
For almost all professions, you can work in that profession after getting a degree from any accredited institution (or often even an unaccredited institution.) Almost all schools are accredited. Virtually every (probably every) public university is accredited and they usually have very low admittance requirements, low costs, and generous scholarships. In many (most?) states, high test scores or a good high school GPA get you a free ride to an in-state public university.
Community college is a good way to get the first two years of a four year degree, or for an Associate's degree that, depending on your field, may be sufficient. They generally also have vocational programs.
You could most certainly become an aviation engineer, architect, etc. by going to almost any school.
The debt story is vastly overblown in the US - it's a serious problem, but mostly among middle-class to upper-middle class families who allow their kids to select the most prestigious and expensive schools, regardless of their academic qualifications, chosen major, or ability to pay. Even in 2017 you can easily get a four-year degree from a good accredited institution and graduate debt free, even if you're not an academic superstar.