<p>You should pick one of Chemical, Mechanical, or Electrical to go into a Bio(Med)E grad program. Pick it based on this:
Chemical if you want to work with the biochemical side of the work. Tissues, cellular level, etc.
Electrical if you’re more interested in making electronic medical appliances. Designing tools similar to the AED and the like.
Mechanical if you’re somewhere in the middle on the issue.
As long as you take a core of a BioE undergrad (about 4 classes, which means maybe 2 electives), you’ll be fine applying from a different engineering major.</p>