Most of the people that you interact with as a physician aren't doctors. It's silly, and frankly, juvenile to suggest that a person can't help you get into medical school simply because they don't have an MD/PhD/DO degree. If a person can attest to your hard work, manual dexterity (a somewhat valuable skill to say the least if you plan on entering ANY kind of surgical field), discipline, and people skills, then you would be a fool NOT to ask them. You get six shots to have someone else sell you.
I think that you pick six people who can write you the strongest recommendations. I think that, yes, most of them should be academic. But, I don't think it's a bad idea to ask someone who knows you as a person, outside the stresses of classroom to write a letter for you.
Talk about the emphasis on all the wrong things. Music teachers are one of the most vital, yet underused and underfunded resources in American schools. Music in education could be the single greatest thing that saves schools. Music in education leads to higher scores in math and science, a greater creative capacity, and lower rates of behavioral- and attention-related disorders. It gives children a goal to reach toward, and it gives them something to be proud of.
I'm willing to bet that there are very few people on this board who can name something that they started doing in elementary school that they're *still* doing. I'm also willing to bet that, if the OP's piano teacher *was* a music professor, then people would feel a lot differently. But, because there are only so many piano professor spots, and a lot of really good piano teachers, they can't all have letterheads.
Adcomms don't ask for 3 letters. Pre-medical committees who write your composite ask for 4 to 6 letters. At least, they did at Big State University with 2,000 pre-meds. And if they're willing to read 'em, I'm willing to get 'em.
Don't listen to the gunners, OP. You're doing the right thing.