It's good that you have your friend there to give that bit of support when you really needed it. And there's nothing to feel bad about from bursting into tears there - if anything that was absolutely the right place to do so - it's a clear demonstration of how you feel to a medical professional, who's there to help.

As turquoisesea said, could you ask them to schedule any appointments to be either before/after work, or during a break period?