Dear Emily, as a biomedical engineer, I work on medical problems every day. Examples are: developing decision-aid systems that predict complications for newborn babies in critical care units, assessing the level of rheumatoid arthritis in patients using infrared cameras (that measure temperature, therefore level of inflammation), and seeing if the treatments are working. In 30 years, I have never had a boring day. You can combine engineering with medicine by doing a bachelor in biomedical engineering or doing an engineering undergraduate degree in electrical, computer or mechanical engineering, then a Master's degree in biomedical engineering. Many universities offer these programs.
As for math and science: Engineering uses math and science to solve problems, so it is a good idea to study these subjects. One does not have to be a genius at these topics, but get a solid base to be able to work on problems. As an engineer, the math and science are not in my face every day. Mostly I use softwares and techniques that already exist and plan experiments that will answer a research question, analyse the results and make decisions on future development.
Your mom is right, you seem to have what it takes to become an engineer. The main thing is to have a goal and go for it the best you can. Best wishes for a successful career!
Monique Frize, P. Eng., O.C.
Professor and researcher, Biomedical engineering Carleton University and University of Ottawa