I dealt with anxiety during the end of my drinking and well into sobriety as well Rupert, I know exactly how you feel. I turned around from business trips and cancelled meetings, etc in the past. I personally view my anxiety as a completely separate condition that I must treat separately from my sobriety - and i've used self help, therapy and even a medication. A combination of a lot of those things has really helped me keep it to a manageable/livable thing. I'd suggest seeing a therapist or counselor if you have the option.
My anxiety was REALLY bad in the first month or so after I quit drinking, not sure where you are in your journey. But yeah...a lot of this stuff is unfortunately normal for anxiety. It's absolutely treatable though.