I've definitely been in a similar position before - needing to see someone for anxiety, but being unable to access them because of the anxiety. Even though over the years I've been able to get the anxiety down to manageable levels I still feel all of these worries "Its the fear of going, the worry about what they'll say, the cost, I
have significant scars both emotional and physical that I don't even
know how I would begin to tell someone about".
I find that what helps me is to "over-prepare". I always call ahead to figure out prices, or check their website, or email them if that's an option. I've definitely done practice runs at getting to the place, so i don't end up getting lost on the day of the appointment. It's also possible that you could practice with some of the questions that they might ask, and prepare some kind of script. What's helped me so much in receiving the help I needed was tracking my symptoms daily, rather than guessing them when I was asked, as it means if I'm having a rough day I can hand over my mood sheet & my sleep sheet for the past couple of months without having to struggle through explaining it.
I hope you can manage it somehow, and I'm glad you're getting support through headspace!!