I won't bother fighting over your embarrassment, you obviously want to be embarrassed so be it but I would like to point out a few other scenarios?

The person on the phone just before you called was a real pain in the a%& and the appointment maker is lousy with her own emotions so let her annoyance at that person seep out at you.

The other desk clerk was trying to get her attention while she was on the phone with you and distracting her and she didn't like that one bit and was really annoyed. . . at the other clerk.

She got up on the wrong side of the bed this morning and doesn't have a dog to kick.

She is an annoying person and doesn't realize how annoying she can be.

It wasn't the doctor was it? Why would anyone else "care" who called on the phone and made an appointment? One appointment person is pretty much like another appointment person. Yes, you do need to be worked into a too busy schedule but that it's too busy is their problem/fault, not yours. They're annoyed at working anyone in, doesn't matter if it's you or the next person who calls with an emergency.

I hope your doctor can think of something today to help you weather the wait and/or that your partner is coming home soon to hold and comfort you and thinking about that moment will give you some comfort now.