I know there was some discussion about SWA joining the list of ME participating airlines, but I do not believe it has officially happened yet. You can still check in at your hotel, but they wont handle the luggage. you'll have to do that yourself.
At the 24 hour mark, go to the front desk (or maybe concierge, depending on the hotel), and ask if they can do online check in for you. Have a print out of all of your confirmation numbers to make it easier for the clerk.
You ca also do a wireless check in if you have a internet enabled cell phone. Go to the SWA web site, select Travel Center and then Wireless Access for instructions. You will be able to check in and get your boarding group assignment and then print out your actual passes when you get to the airport.
Good Luck...