Hi! If you are having a reaction to the anti-biotics, call the doctor that prescribed them and inform him of such. That's important to do especially if you are reacting to the medication.
A good trick for nausea when on medication or having a headache is to put ice on the back of your neck while laying down. (You can make an icepack with a washcloth and a handtowel). This really is effective!
Over the counter medications can help with headaches but too many of them can cause what is known as a rebound headache. You might want to mention to the doctor when you call about the anti-biotics that you aren't getting any headache relief. Ask what he recommends.
Did these headaches just start recently due to the sinus problem? If so, once it resolves they should also! That's the good news!