I'm not certain what type of work you do and certainly am not asking as your preference to not have to go into details, I can respect. I'm trying to think of some examples as I start to type as my workplace can certainly carry with it a multitude of stressful moments of a variety of sets of circumstances. I do have anxiety that noone would begin to suspect of me. So as someone who hides their anxiety and has sorted out for myself ways to handle stress and my own way of addressing criticisms I'm going to try to give some advice.

I must admit it took some book reading, article reading, CBT and a willingness to change my own sensitivities.

Try to stay grounded/centered in the moment when you can. Take a deep breath or two before addressing the request or question. Stick to work related topics the best you can. Try to picture that as anxiety ridden as you feel that the other person is just as anxious/stressed. Repeat requests back for clarity and as a way to allow your brain neurons to connect for clarity. Grit your teeth in a forced smile if the person just really seems to hit some nerve deep breath at the same time.

Books like John Lee's "Facing the Fire" can help. That one I highly recommend because it really helped me connect the dots. All books about being an adult child of dysfunctional homelife, etc were insightful but that one helped me see where and why my emotions felt like an overreaction. I wasn't an angry, angry person before but my emotions never seemed to line up.

I'm not sure what else to add at the moment but I'm confident others will have some other insights.