I'm so sorry to hear about your anxiety. You've gotten lots of good advice. Don't discount the meds that are available to you. Have you talked to your doctor about it? If you don't want to be on meds all the time, there are anti-anxiety meds that you could take that day, as long as you have someone to drive your baby to the vet.
Can your DH make the appt? Take him/pick him up? That might help, you can be in denial until he's home.
You can do it!