You were right!
Okay, of course you were right, it's insulting of me to have an epiphany over it. But you told me to slow down, and I didn't think I could, but I did! I just finished a nice slow 20-minute jog.
To be fair, I was interrupted at the 13-minute mark by a delivery guy -- but at no point did I have that dragging "I sincerely can't survive another 30 seconds of this" feeling.
Gonna build back up to where I was before -- gonna graduate from C25K -- and my speed (such as it was) can come back when it's ready.
Thanks, everyone! I think my confidence is restored.