Hi Elly:
There's a free transportation system between terminals at JFK called Airtram. you can find it right outside of every terminal building. Travel time between those two terminals should be around 10 minutes.
You can check with Korean, and most likely they do have a baggage agreement with American Airlines. So make sure they check your bags all the way to your final destination upon check in for your first flight.
HOWEVER, please keep in mind, that you have to clear Immigration and customs at the first port of entry into USA, in this case JFK, this means you have to pick your luggage up in New york, go through customs, and then give it back to the TSA (Transportation Security Authority) after clearing customs.
Hope this helps, and welcome to United States.
Hi Elly: There's a free