Re: Sinusitis
Sounds like a fob off to me.
A swelling is indicative of an infection of some kind so throwing antibios at it is a way to kick the can down the road and see if that clears the infection up. It may do, then again it may not. If not you'll be back to the doctors of course.
Either way the doc gets to kick the can down the road and move on to his next patient.
If you hadn't been to see the doc then I would have recommended making a drink of blitzed lemons (whole lemon, pith, peel etc) and a chunk of fresh ginger with a little hot water and honey. That would have boosted your Vit C levels and other nutrients and boosted the immune system.
If you're going the antibio route regardless then it's too late for natural remedies. You then need to concentrate on repopulating your gut flora which will be destroyed by the antiobios. So plenty of bio yoghurts and the like.
I presume you will have been given Amoxycillin in some form. General purpose, wide spectrum, "I haven't a clue what is it" antibiotic.
Best