I don't know if this is totally true, so don't take my word from it, but I think it makes sense:
One of my friends told me that if your school has a letter service, go ahead and tell them to send all the letters you want to the school you want. Schools may say they only want 3 letters, but if your letter service sends them more, they probably won't take it out on you, b/c letter services often make mistakes.
I guess if you really want to be safe, you can call the school and ask for permission to send an extra letter, and take down the person's name if they say you can.
Another thing is that often, later in the application process, you can always send an extra letter. I've found that it's often good to send in additional letters to strengthen your file, so the opportunity should present itself.
In any case, give them at minimum, exactly what they asked for. If they want letters from 3 profs who taught you in class, give them those. Add the doctor's letter (the one you're shadowing) if you like, as a supplemental letter.