I have a nephew who is an MIT PHD graduate in /aeronautical engineering and now is a professor, also, I have a kid of a friend who have just graduated from UCal UG in aeronautical engineering. Based on my knowledge, it is almost impossible to find a job with only an UG degree in aeronautical engineering. I took the kid’s resume to a friend who had retired from NASA and he said that they do not hire BS in aeronautical engineering. Same thing as an UG BME, you will not find a good job with only UG BME.
Perhaps you should choose a school that fits you first, study two years there to “find” yourself and job prospect before deciding.