Would nursing be a good career for me?

i am a freshman at a very good engineering school. i am majoring in biomedical engineering and i am pre-med. recently, i've been thinking that i would make a much better nurse than a doctor or an engineer. i have good grades, ~3.7 gpa, but i don't think that i want to spend my life in school, at a desk or in a lab. unfortunately, my school does not have a nursing program so this is a very difficult decision.

i love taking care of people and when someone is upset or hurt, i do everything that i can to make them feel better, even if they are not someone that i particularly like. is this what makes a good nurse?

i am also considering nursing because it will provide me with a little more financial and personal freedom than being a doctor would (i.e. not tied to my loans, not missing out on most of my twenties/family). is this true?

the one thing that i am very concerned about nursing is that some people look down on it, and i have heard from many sources that nurses are treated like dirt.

i am an engineering student because i enjoy problem solving, math and the way the body works, does being a nurse involve any problem solving or is it mostly repetitive?

i am very confused so if anyone could answer some of my questions, it would be greatly appreciated .
I can appreciate your efforts to ensure you have a meaningful career. However, have you seriously investigated the biomedical engineering field???? In my experience, they are very active in patient care environments - very crucial in today's highly technical clinical environment. Working conditions are much more pleasant, hours more 'normal'. They have much better long-term career prospects (salary compression, lack of promotion opportunities, etc.) than nurses.