Chemical engineering is worth pursuing as well. Many schools offer a biomedical concentration in it so that is worth checking out as well. As the above comments mentioned, it depends a bit on which type of specialization you wish to pursue in med school as well as the program path offered at your school. Personally, I feel biomedical engineering fences you in a bit too much. I know many of my peers in chemical engineering who went on to do pursue med school. They all did the biomedical concentration which had them focus more on biological topics, additional organic chem courses, and a pharmaceutical plant senior design project. This would provide a great fundamental background for entering medical school and would allow for the fundamentals for any of the paths. If you have the option of taking electives, you could take mechanical engineering electives which would augment your credentials for creating mechanical devices used in medicine.
Additionally, I've been told the rigor of engineering prepares you best for med school regardless of which discipline you choose. So know no matter what you cannot go wrong (unless you go I.E.-that's just my personal bias though).
Definitely take up Hagan on his offer of networking as that is going to be critical.