Soliciting advice about current work situation. Thanks.?

I am a little bit confused about the professional realm of my life right now. I've been working as an energy data analyst for a consulting firm headquartered in Fairfax, VA. I've been increasingly bored with the job. I think part of is that I've grown during the past several years. Another part is that the job was never meant to be all that challenging in the first place. In some ways, if you think about it, it's the typical government job. I really can't stand the boredom, and I don't want my brain to keep rotting. I've been asking around to see if I could be transferred to another business unit the company, but my project managers at this business unit insist that I have a place to fill and responsibilities to carry out in this business unit. I mean, they're right in the sense that I should be here at least part-time. And they're not jerks to work with either. I enjoy working with them; it's just that I am not finding the work all that challenging. I've thought about several other options, however, to make sure that my brain doesn't rot nor skills continue to deterioriate: (1) Should I take advantage of the company's tuition reimbursement program to fulfill medical school requirements and apply to medical school? I feel that people in the medical rpofession are constantly challenged to grow. I think that it could be a very fufilling (albeit stressful career); (2) There are several areas that I'd like to pursue within my own line of business - oil and gas accounting, as well as smart grid projects. I think that I'd enjoy the coursework in these areas, and I will continue to work in my current job, (3) Should I switch to another business unit in the company altogether that'd challenge me and help me learn new skills? I am also applying to other jobs at the same time, but would like to do something concurrently with that. Any thoughts? Thanks.