My S is biomedical engineering...do your best to apply by the first week of October. As earlier poster said, if you are auto-admit then getting into your first major completely depends on when you get your app in and whether the major is full. Since BME is very small, it does fill up quickly.
Also, as an earlier poster said, majoring in chemical, mechanical or electrical engineering and then adding some BME courses here and there...or studying BME in grad school...is wise.
Just finish that application!!!