My pediatrician said I was 5"8 but I keep coming up as 66 inches whenever I measure myself?

Different methods. I believe i'm 5'9, but i keep coming up 5'7 and 3/4 at the doc's. Not sure what to do about that. But in your case, they may be measuring you with shoes on, or that when you do yourself, you position the tape differently than they do the bar or wall gauge. Plus you may be slouching just a bit while that one nurse can always get you to stand really straight in the office.
Someone messed up! Hard to say why it happened, but somewhere along the line, someone probably misread something, either you or your pediatrician. Next time get another measurement.