Nandz, hope you're starting to feel better.
Keep up with the cold packs until your swelling goes down. Heat would dilate your blood vessels and make the swelling worse. Prescription pain medications sometimes have anti-inflammatory properties, and OTC ibuprofen-based medications (Advil, Motrin) are also good anti-inflammatories.
Also, watch out for dry socket. If it is very painful or the pain gets worse instead of better, especially if it hurts when you breathe in, then you might have a dry socket and you'll need further attention from your dentist or oral surgeon.
Hope you have a quick recovery!
Trinity