From what you describe here it does sound like you have some spillage internally (not an OS problem).
First your lucky you had a key board skin on your system when you spilled your drink. I'm sorry to say you should not use it as it does stop the flow of air the system needs to cool its self. Your drink has both sugar and acids which over time will cause damage (corrosion) and burnout components.
The keyboard skin would have funneled your drink into the areas along the keyboard and case edge this is where the drink may have leaked in. Try popping the key caps off around the edge where the drink spilled the most. With some distilled water (not tap!) and some cotton swabs moistened (not wet!) see if you can clean up the last remains of your drink. Hopefully it didn't go any farther in from this direction.
As for the fan grill along the back edge I suspect thats where you have some work to clean up your drink from the main logic board. Follow the steps outlined in this IFIXIT guide MacBook Pro 13" Unibody Late 2011 Logic Board
As you will need to get to both sides to inspect and clean the drink and any corrosion you find. Again you'll use distilled water with the cotton swabs but this time you'll also use some 85% or better Isopropyl alcohol to wipe down the areas a second time to help remove the water (acting as a dryer) and to remove any oils that may have been present in the drink. Take care not to snag the swabs on the small components as you don't want to pull any off. You may need to use a small soft brush to scrub down any corroded areas again be careful! You can also use a can of can'ed air as well to help in drying. Don't forget to wash out the heat sink fins as well.
Post any pictures of areas that look bad so we can see the damage. We may have some ideas how to deal with them. - Good Luck