I'd go with the doctor on the 16th.

In the future, I would make the referring doctors make all the arrangements, you show up. It shouldnt be up to you to keep following up just to get into someones office. Most doctors handle all the arrangements and call you with time/date to show up.
Writing a letter would comfort you but the office isnt going to do anything about it. Only letter they will pay attention to is one from a lawyer.