Would a CT scan without contrast show a brain tumor or evidence one was there? What are the chances it won't? Doc not concerned but my anxiety is :/

See long answer. Ct without contrast is largely indicated for acute hemorrhage or infarcts. It may not show more subtle tumors. Mri with contrast is much more sensitive in the correct clinical situation. Talk to your dr. To see if further imaging evaluation is appropriate.
CT can miss tumors. Ct is good to check for mass effect, swelling, and shift. If there is a tumor, may only see mass effects. Best to screen for mass effect by ct w/o contrast, and if symptoms persist brain mri.