Can a negative ct scan without contrast of the head miss a brain tumor causing headaches?

Yes, it can. Did you go to an ER with H/A & they did a knee-jerk don't-sue-us CT scan which was normal? If you've had H/As for at least 3 years, the chances of finding a tumor on brain imaging are no greater than for someone with no history of H/A. Are your headaches of recent onset, relentless & worsening? If not, you can find something else to worry about, like the outcome of the 2016 presidential election.
Be reassured. The CAT scan did NOT reveal a tumor, so do not focus upon that type of problem! Instead, find out the type of headache you are experiencing so appropriate treatment can be initiated. If migraine, preventative measures exist, but triggers could involve neck, jaw, dentition, sinuses.