the general advice for anything where tapping hurts is to gently place your finger on the point and breathe deeply on each point, in and out. Do the whole Classic EFT Protocol (which includes the finger points) and do it round and round, meaning don't stop after one round, go straight into the next.
When I was researching EFT I played with various ways to stimulate the points and remember one occasion where I used an ice cube.
Now this may not be the right thing for your sinus headache but perhaps touching a crystal or a smooth pebble to the points, or something warm might do the trick for you? Try out different things. I used to have bad migraines and found that even if something didn't work it was better than just lying there feeling miserable, and especially at the beginning of the attacks when the fear of the pain to come would cause further stress. Eventually I found the ice cubes and that did the trick for me; so perhaps you can find something too.
One last tip - when I could catch the migraine very early on, the very first symptoms, plain tapping on stress often did the trick to relax me and clear it up, so the sooner you can get to it, the better as well.
Hope that helps and good luck to you,
Author, Adventures In EFT & Advanced Patterns of EFT