Would a sinus x-ray likely show a bad sinus infection? or an infection in the sphenoid sinuses?

Maybe and no: If plain sinus films suggest an infection in e.g. the frontal sinuses, the usual next step is a CT scan. Diagnosis of sphenoid sinusitis usually requires a CT or MRI scan. No modern clinician would rely solely on plain radiographs anymore,

Yes, a sinus X-ray: series would probably be abnormal with severe sinusitis. With less severe cases, it might look normal.