How is a brain aneurysm misdiagnosed as sinus problems?

If it is big enough: You are most likely describing a carotid artery aneurysm possibly a cavernous sinus aneurysm which if it became big enough, it can erode the bone and enter into a sinus because they are right next to it. I would need to know more to help you better. But in such a case, the Ear, Nose, Throat surgeon needs to be very careful if they go into your sinus as it could be life-threatening.