Dear Gopika, You have many good questions. In the early days of biomedical engineering, one had to major in a more traditional department because the field was not well known or well accepted. Today, that is not the case anymore and you can major in biomedical engineering and people will know your degree. Chemical engineering can be actually quite different than chemistry class in high school so i would still keep an open mind about it. Other options you might like include materials science and engineering or mechanical engineering.
I bet you are - or could easily be - more innovative than you think. In college or before, take some design or design engineering classes - innovation is a process you can learn. Also - take a class in something very different - innovation often occurs at the crossroads of fields or by taking an idea from somewhere and applying it to a new field.
As for classes - AP classes can be nice in getting a good start in college classes but the health sciences classes sounds different and therefore interesting. I don't think you can go wrong either way so may be good time to take what you would enjoy the most!