The important issue is that you have your possible sinus infection treated fully without any residual symptoms prior to your operation. There is no harm in having residual antibiotics in your system. In fact, most plastic surgeons prescribe antibiotics before, during, and after surgery.
I think you are safe to travel before mommy makeover without significant concern. If for whatever reason, you do come down with a cold, sinus infection, etc.. then the critical thing is to let your surgeon and anesthesiologist know so that they can decide if you are safe to proceed with...
Removal of drainage tubes after tummy tuck may give some relief, but the drains typically do not cause a tremendous amount of discomfort when inside the tummy.