Don't use a straw, wear that ice pack thing like crazy.
I fell asleep for 14 hours after surgery with the icepack on constantly and I had absolutely no pain or discomfort during recovery. I'm just attributing it to the fact that the ice probably helped a lot with the post-op inflammation and since I was sleeping my surgery sites probably had enough time to make some hella strong clots.
tl;dr, go to sleep with the ice pack on right now