To start, giving it to God is a great plan, as with most every challenge. However, even though He may not immediately take it away, hindsight is always 20/20, as they say. I always look at it this way - while we still get anxious, we have gotten through EVERY SINGLE anxiety and panic episode in our lives up to this point, this one will be no different.
I am in a relatively good place with my anxiety. Don't get me wrong, I have had it for more than half my life at this point and do have some symptoms on a daily basis, several times a day, but it is something that I have learned to deal with and cope with. While I don't consider anxiety to be a disability per se, I can relate to how those with a disability get on with their lives in spite of their particular challenges during the day. I think this is how I have been able to be on a pretty even keel for at least a good 5 years now. In my younger days, I balked at my great doctor saying I will have this the rest of my life. I spent so much time working and hoping for a "healing" that I looked right past the fact that he was not saying "You will be housebound and terrified and panicking every day for the rest of your life". He actually said what he meant - you (I) will deal with anxiety for the rest of my life and he has been right. I have. The difference is that It doesn't control me (much) anymore and I am now an unwitting expert at living with my anxiety disorder as opposed to not living because of it, if that makes sense. When I finally accepted the fact that my doc was correct in his statement, I think it freed me up. I do think that total healing is possible, but since anxiety is a common thing that every living non plant thing experiences as a part of principal biology, it is impossible to ever be completely "free" from anxiety.
Anyhow, I digress. I too very much dislike doctor's appointments, mine or loved one's and even non anxiety folks feel this way, so you shouldn't feel abnormal because of it. As mentioned before, you will get through the anticipatory anxiety (this is the worst, isn't it?) and the anxiety of the task as you have every time before now. Since you know that..maybe this can give you confidence, which is always the antidote to anxiety. Godspeed to you and God Bless.