A good biomedical engineer should be interested in solving biological or medical problems. Some people think of new prosthesis devices or therapeutic delivery agents as examples, but you should not limit yourself to what you have seen. You are only limited by your imagination.
There are several skills that you will need to become a true engineer with the ability to solve those questions. You will need to use a lot of math, and understand the fundamentals of physics and chemistry very well. Those subjects teach you design principles an engineer needs. And of course, you need to understand the biology of the problem you are trying to solve.
Some well-renowned biomedical engineering programs in the country include these: Johns Hopkins, UCSD, Georgia Tech, MIT, UW (Seattle).
After 4 years of college training, you would have many job options as a biomedical engineer. One or 2 more years of masters training might start you at a higher salary. These job functions can be engineers in a medical device company or research associates in biotechnology or pharmaceutical companies. You may work in research and development, manufacturing, or quality assurance departments. Some people prefer to go to medical school or graduate school after college. Those will take another 5 years before you become a medical doctor, or a Ph.D. who can become a professor or work as senior engineers/research scientists in the companies mentioned above.