Don't bother with the letter. If the doctor needs help writing the letter, then all indications are that he doesn't know you well enough to write a strong one himself. What you will end up with is some cookie cutter letter that won't hold much weight at all with an admissions committee. Although, if the doctor knows you well and is asking you to write the letter then give it to him to review and sign, then that's a different story.
In the end though, I would just forget about it. Putting down the shadowing experience on your AMCAS application is fine, but getting a letter from someone who you basically just lurked naively behind for however many hours is just a waste of time and paper.