Sunburn?

Is it possible to sunburn your lips? My lips have been sore and chapped as hell for about a week now and the only explanation I can come up with is that I sunburned them. Either that or it's from my 'other job' walking the streets down by Seatac..... Anyway, no amount of chap stick seems to be fixing the problem. They are cracked and a little swollen and it's really starting to get unpleasant. I just hope the worst of it's over.