I have morning headaches for the last month. Should I have an head CT?

Depends... ...On a number of factors.Does the headache wake you up at night?Is it worse when laying down, straining, or coughing?Do you have other neurologic signs?Is your headache worse with loud noises or bright lights?Family history of migraines?Is it related to other issues -blood pressure, medication use, illness, diet, heat, hydration, ? Your doctor should see you soon and determine the need for a ct.
Maybe/not. Only a thorough history & physical with your physician can begin to decide this issue. Do you need a MRI instead, or a sleep apnea evaluation? Do you have physical findings that would point to that need ? The problem with advanced imaging is understanding its limitations & applications.X--rays, CT's or MRI studies are seldom necessary for proper headache evaluation, but it happens.