Corki is not OP imho, although I only played him once. He is your typical damage dealer, so very low hp. You shouldn't have any problem nuking him from orbit as annie.
His ulti gives him bombs every 10(?) seconds, he can carry up to 7 bombs. He can pretty much spam the bombs none stop because the cooldown is like <1second.
They have a pretty little hit box so they are easy to dodge, just make sudden movements so you startle him!