Have you talked to the doctor? I'd give them a call, first thing.
You're assuming your sore throat is due to post nasal drip (PND) and it may be, but it could also be caused by the nodule since it's so large. If it "is" PND, you may have gotten an infection, in which case you'll probably need an antibiotic anyway. You might as well get it now and try to get rid of any infection before it gets too bad. If you can get on an antibiotic now, you may not have to postpone the surgery since you have someone coming to help with childcare now. They should understand that it's not easy to change flight plans without paying extra and other people can't always rearrange their schedule to match yours.
I got an infection caused by PND last year, just prior to flying to visit a sister who has immuno-deficiency problems. They knocked out my infection in a couple of days with shots in the behind, combined with oral antibiotics and I was able to proceed with my plans.
Good luck and let us know how it turns out.