Why can't you make the appointment yourself? If you want to see a counselor and your wife has agreed to go, then make the appointment. By putting the responsibility on your W, you're setting up a power struggle between the two of you, and actually putting yourself in the role of parent. IMO.
Usually one person in the R has to take the lead at first and you're it.
BTW, I totally understand your W not wanting to make phone calls because she is introverted. I am the same way. I was interested in seeing an individual counselor a couple of years ago and it took me about 6 months from when I got a referral from a friend to when I actually called for the appointment. And this was something *I* was interested in doing, not something my H wanted me to do.