And, if there's any glitch in the process, as a business class passenger you can use Delta lounges (called Sky Clubs). Go to the nearest one as shown on any airport map or the overhead signs. There's at least one in every ATL terminal. The agents at the desk there are rebooking experts. They will take excellent care of you.

You might also want to download Delta's app for Android or iPhone, if you have a phone that works in the U.S. It's the best way to keep informed of flight status and changes.

As regards picking up your bags: that happens pretty much everywhere, worldwide, when you need to clear customs and immigration. The point at which that happens may vary from country to country, in the U.S. it's at your point of entry, but the concept is the same: when you go through customs, the customs authorities may want to look into your bags. They usually won't do that, but they want to be able to. Hence this procedure.