Medicine, veterinary medicine, pharmacology, pharmaceutics, pharmacy, chemistry, biophysics.

You might want to get into details for the professor's research to find out more!

Rosemarie Martinez "Drug Discovery" itself is a very broad term, which encompasses many approaches or disciplines as Adam B Shapiro has indicated. Ideally what you should be asking yourself is what aspects about drug discovery do you find interesting? Structural aspects relating to the actual structure of a drug target? Or the chemistry of drug design or pharmacology? mode of action studies? Once you have some idea of what you find most interesting or exciting then look at published literature or research that are done by specific faculty at the university that you are wanting to apply to. Most graduate programs offer course work initially then you would do lab rotations in the labs of the faculty that you are interested in. So you would obtain a degree in "pharmacology or biochemistry" but you would have specialized expertise in a specific approach in drug discovery depending on that faculty member that you have joined during your degree. For graduate school its more about the faculty expert rather than just the name of the degree.

Biochemistry itself is more than just bio-and chemistry, it encompasses lots of specialized fields. Some have been mentioned above and I would say they are still subdivisions of biochemistry. When you talk of nutrition and dietetics, you find nutritional biochemistry; when you talk of immunology, you find immunochemistry under same subject, all and all like that. Importantly, the world have moved into molecular diagnosis, so I would advise you seek a new challenge in this area where your biochem basic knowledge could be useful to chose a favourable sub-specialization such as; nutrigenomics, proteomics, oncometabolite studies et cetera. All here, to mention a few.