Also try ice for the inflammation instead of heat. I know its not fun on the neck but may help more then heat :-)
I'd have to agree. If you don't feel better in a week, than I would see a doctor. You may have just bruised something or it may be more serious. If your face hit the ground pretty hard, you may have damaged the vertebrae in your neck. You would need an xray or MRI to rule that out.
Ibuprofen is anti-inflammatory and so it should help you out. Does it? If not, then I think a trip to the doctors would be a good idea especially if there isn't any relief in the pain symptoms after a week.