Rheanna has made some very good points. Doctor's notes are always a good idea.
If this is a one time thing, and you usually never miss work, I'd tell your boss to shove it, and get a doctor's note if you have to. Who is he to say how bad you feel?
If this is a chronic thing, how much work have you missed? If it is a lot, then you need to emphasize to your doctor that your sinusitis is interferring with your work. Remind the doctor how long it has been going on. They often read just the tops of the charts and forget how much time has truely passed. If you are dealing with just a regular doctor, you need to get a referral to an ENT as soon as possible. If you haven't done so, you are long overdue for a CT scan of your sinuses, and perhaps allergy testing. You might need surgery or allergy shots to resolve this.
As far as your boss goes, he makes me angry. Obviously, he has never had to deal with sinus problems. A nicer person would say they wouldn't wish it on their worse enemy. I guess I'm not that nice. My sister called me a whiner for years, until our family history finally caught up to her and she developed allergies and sinsus problems. Instead of sympathy, I felt vindicated.
If it is a chronic problem, tell your boss that you are really ill, and even though you have been given a diagnosis of sinusitis you are looking into other diagnosis because you truely feel horrible. You don't actually have to do that, just make him think that you are doing that. For someone like him, who thinks sinsusitis is no big deal, that will impress upon him that your situation is serious.