"I can't talk now, I'm totally thronged." means swamped with work. "I came in to work and was thronged with emails."
Common expression in Wall Street law firms. Originally from Old Norse. cf Icelandic þröng, etc. (narrow, tightly pressed; compelled, forced in the sense of being pressed to do something );
trang (narrow), Swedish trång (narrow, tight). All probably related to the Standard English
throng (crowded, to form a tightly-packed crowd, etc.). Perhaps from Yorkshire dialect. Variants:
thrang,
threng.
