Airline credit card situation advice?

Hopefully this post is relevant to travelitters. Is there any way I can get my rewards points in time to use them on a New Year's Eve flight, or did I get suckered?

I signed up for a Southwest credit card a few weeks ago (for the 50k points). Two days ago, it arrived in the mail, and yesterday I made my first purchase with it. I called to see if I could have my rewards points applied, but kept getting bounced back and forth between Chase and Southwest, but ultimately, it seems that the soonest I can get my points is 1/11, after my first billing cycle, when Chase tells Southwest that I did make a purchase.