I'm glad to hear that you enjoy both biology and math, and are also interested in engineering. That certainly suggests that biomedical engineering might be a good career choice since it combines all three. Take a look through the Engineer Girl pages to check out the types of projects biomedical engineers work on, especially the non-academic types. Forbes Magazine just recently named Biomedical Engineering the #1 most valuable college major, but you should make sure it's a good fit for your interests.
As far as experience for college applications, one engineering activity that comes to mind is the FIRST robotics program. It's not directly biomedical engineering, but robotics applies to a range of different problems. I've not been involved with admissions, so I don't know how helpful it is to college applications, but FIRST is designed to engage in science, engineering and technology so the experience is generally relevant.
Thanks for your question and good luck!