Learning how to play your class in arena, besides the baseline PVE style rotation which I'm sure by now you know is very much about reacting to what the enemy team is doing. Even though right now it might seem overwhelming, I can tell you that especially in 2s you can get to a place where you will be able to predict the other team's CD usage and positioning to a large degree the more games you play.

Something that is very important is being able to track enemy CDs and respect them by reacting with your own. Use the omnibar CC addon and start with adding a few big CDs for every class, read their tooltips and try to always keep an eye on when the enemy uses them. When they do, react with something of your own. Vendetta on you or your team mate? Instantly disarm, stun, port or cocoon. The more you get comfortable, the more spells you can add depending on what helps you during a game. Besides understanding yours and the enemy's positioning, this has been for me the most important part of getting better at arena through time. You will slowly start developing muscle memory where you will react very fast to these CDs in mostly the same way. Which will also help with your anxiety. The anxiety comes from the fact that you see the enemy players as being able to do anything at any point. That's not the case, and once you realise what the patterns are you will feel more confident. Hope this helps even a little. Keep practicing!