If you are looking for book recommendations, How to Win Friends and Influence People is still a good foundation. Books by Berné Brown are really good.

The short answer is: your anxiety comes from the fact that you are focusing on how awkward and shy you are. When you notice your attention going this way, try to redirect it toward curiosity about the other person.

(I find that in order to do this, I still sometimes need to clear the air by stating outright to the other person that I am an awkward nerd.)