Which is correct? 1. for nagging me to apply; or 2. for nagging me into applying
Solution 1:
Mr. Leach above is quite correct. The only salient difference is the outcome of his nagging. Because of the outcome his nagging you to apply was not enough but his nagging you into applying did the trick.
Congrats on your success wherever you are. Here I would have said don't mind the nagging. It's the American way.