Most of my recent anxiety has been rooted in the workplace as well, so I can relate. I would be at work constantly comparing my performance to the performance of others I work with, even if we didn't really have the same job. I would think that everyone around me is doing better at their job than I was, and it didn't take long before I started thinking that my bosses must hate having me around and that my peers were annoyed with what I considered to be "My Underperformance". I didn't say much at meetings because I had chisled away at my own self-esteem for so long.
I found out that the truth was that everyone at work was feeling stressed out, not just me. The company I work for has been going through a lot of changes, so roles and procedures were constantly being adjusted as well. I hold myself to a high standard, so I spent a lot of time beating myself up and convincing myself that my co-workers and managers were sick of having me around. This was all false. I was tearing myself down by exaggerating the truth. Nobody was as hard on me as I was.
My therapist told me I should take a moment and think about what proof I actually have that others are thinking negatively of me. Whenever you think "I don't want to talk on the phone because others will hear me and judge me", follow that thought immediately with "where's my proof that they are judging me?". I often found that I had no proof. This has helped me in many cases. Your struggle may be different than mine, though, so confide in your therapist. They can help you through it.
The decision to tell your management about your situation is completely up to you, but I will say that I believe communication is the best way to solve any problem. Letting a situation fester in silence only makes it worse. You don't even have to tell them about GAD. I eventually told my bosses about my struggles in the workplace and it helped a lot. If you decide to tell them, be careful not to make it a pity party, and don't make it about other co-workers. You should make it about your performance struggles and how you can improve on the current situation. Now you're not looking for special treatment, you're trying to improve and you are seeking assistance. It may be uncomfortable, but at least you've made a professional effort to clear the air and show your managers that you are committed to improvement.
Good luck! And sorry for being long-winded, I tend to be that way!