Joining a casual get-together is not an obligation. However you do want to get out for important self-care matters. I would think an eye appointment falls under that heading. Try to keep the appointment.

Staying home when you need to as part of your stress management can be a good thing. But if it's snowballing into actual agoraphobia, you need to fight against that. It's all about empowering yourself to the max. Going out vs staying home should be choices you make freely, not choices that are made for you by exaggerated fears.