Drug discovery is a really large field. Do you want to be involved in the research laboratory? Or see patients in the clinic? I work in drug development, but in an office where we oversee the clinical trial activities. As you can see, there are many paths to drug development. Typically, a research laboratory scientist has a PhD, and physicians in clinics are either nurses or MD. There are other administrative people behind the scene like me who have anywhere from a Bachelors to Masters in Sciences, or even MBA.
Hope this helps!