"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.