When you post in a thread, that thread gets added to your watchlist.

You have to enable this first: Click Profile > Notifications and Email > Automatically watch topics after replying to them.
See:

I don't understand why anyone would not use the watchlist. You can configure the watchlist to be exactly the same as "show new replies to your posts" by configuring your posts to be auto-watched and adding your posted-in topics to your watchlist. After this is done, you can unwatch topics that you don't want to see.