Is there an artful and sophisticated way to tell your professor that you have nasty anxiety that often gets in the way of your class performance?
Not really. Although mostly because anxiety, in and of itself, is raw and neither artful nor sophisticated. I’d recommend just giving your professor the bare facts - that your troubles with anxiety has undermined your performance and inhibited a more realistic reflection of what you’re capable of doing in her or his class. And ask if there might be some means that you two can come up with to better manage this anxiety and hence provide a more accurate demonstration of your academic abilities and performance.
or you could just paraphrase the above… it’s kind of arty and sophisticated :/