Since you mentioned that you have been in the professional workspace for many years now..
.
.. if still you are finding it so stressful .. as to trigger your flight or fight response..
... then better to talk it out.
.
If not with Mr. A and Ms. B.. then with some mentor or senior within the organisation.
.
But ultimately... in the long run.. if such people or situations keep crossing your path,
.. then only other practical coping mechanism might be to be more assertive.
.
Such things may not be a one off thing or limited to your current organisation/ workspace alone.
.
If you have similar palpitations issue in personal life too or in case this has started affecting you in way more disconcerting ways... then seeking timely professional help in the matter might be optimal.