Usually brain tumors yield some much more serious symptoms than headaches - namely intense disorientation, vision problems, nausea, seizures, etc. Now you don't have to take my word for it, but if you're only experiencing headaches AND a neurologist told you you're fine, then I don't think you could possibly be any more in the clear.
Also, it's important to know that headaches are one of THE most common side effects of anxiety. I myself have had a phobia of cancer as well (especially brain cancer) ever since my father died, so I understand the dread you might feel about this, but trust me when I say you're perfectly well. Chin up! :)