Good for you for flying again! As you can see, you are not alone in your struggles and you have received solid advice here.
I'm guessing you are trying out a shorter flight for your initial foray right?

As a fellow claustrophobic person, here are the things that help me:

-Always fly first if you can, closest to the front and aisle seat. Always helps to have more personal space. I struggle in coach due to the seatback in front of me being practically in my face (and I am short). It also adds to my discomfort to not be able to get into my under-seat bag due to the space being so tight.
-I pay for Admiral's Club annually just so I can have a quiet place to wait for my flight. This reduces my stress considerably. The noise level and crowds in the terminal are hard for me to tolerate when my stress level is elevated. Plus you can have free cocktails if that is part of your self-medication.
-Board last, as others have recommended.
-I think one of the main benefits of first (for me) is that you get off the plane first after landing. Torture for me is being in the last row and taking 20 minutes getting off the plane. It is a huge help to stand up and walk off first and avoid the congestion in the narrow aisles in the back of the plane.

Best of luck and let us know how it goes.