I'm so sorry that you are going through a hard time with this. I have needed to do several of those 3 hr tests- twice (in 2 different pregnancies) vomited shortly after the first hr and had to go back and do it again. Not fun. I second the music suggestion- once I took a laptop with a movie to watch.

How to get yourself there- as you say- at some point you will just do it, because you have to- I find it is often an impulsive moment when I can schedule some medical thing, and then its done... and then its almost an automatic thing that I just have to go. I sort of break it down - or try to just think about scheduling without thinking about actually going. I dont know if that makes any sense or not, but thats sort of how it can sometimes work for me.

As to eating- have you tried using Boost or something like that? I think its often easier to drink something (cold tastes better to me) than stare at a plate of solid food when I have no appetite.

Wishing you the best.