Ibuprofen’s not just a painkiller, it’s also a potent anti-inflammatory. If you have a sinus infection, you have inflammation.
Yes, a sinus infection can give you a toothache. It’s happened to me before.
If you don’t really like spicy food, you might consider trying Sriracha with the rooster on it (if you can find it with a hechsher you hold by). It’s pretty spicy but for some reason it makes you want to eat more and more. That way you could end up eating enough to blast that sinusitis away. Hatzlacha!