Do you generally suffer from chronic headaches? Do you take any medications daily? Do you drink coffee daily? Do you eat anything just before the headache starts?
If you don't generally suffer from chronic headaches I would push for that MRI sooner rather than later. If you do, I would consider rebound headaches, even though its one sided. Does anything make it better or go away.
A short time ago I kept getting a one sided migraine and it would start about 30 minutes after I got up. It turned out I was forgetting to take my beta blocker, which explained why it would go away at night.
I asked the questions about coffee and eating because I have also found foods to trigger headaches and know for me coffee is a bad one. I couldn't figure out why I had a headache each day and then gave up lattes. At first the withdrawl from coffee gave me a headache, now coffee gives me a headache. Its a catch 22. Yeast in muffins and chocolate also trigger migraines (one sided headaches for me). These are foods I sometimes eat at breakfast.
My opinion of the anxiety explanation is that its horsepucky. My experience is that if anxiety is going to give me a headache I have a restless sleep and wake up with a headache. It doesn't come 30 minutes after I wake up.
Oh and the last thing, how hot are your showers or baths. Hot showers, though I love them, trigger migraines for me, make the blood vessels expand. Do you have a hot shower and then get the headache?
Those are my thoughts, though nothing is based on a medical degree all on personal experience. Don't ever be afraid to push doctors or change doctors. Especially when it comes to head pain that can't be explained.