I used to have bad migraines and still have them occasionally.

Mine never responded to a migraine medication though. I get other kinds of headaches that respond to indomethacin. I also have been treated for lung cancer so the possibility of mets is a real one but you don't run off and get a scan for every headache even with a lung cancer history.

There's nothing wrong with getting a brain scan and starting some medications at the same time. Or start migraine medications and if they don't help get a brain scan. Those meds don't help headaches from brain tumours so you can exclude them if the meds do help.

I don't understand your gp's logic except for the part about not prescribing on top of psych meds. For that you might need a neurologist instead of a gp. I hope your old neurologist is able to help you. If not I would try another one.