Have you been tested for diabetes or pre-diabetes?

It could be a migraine? Or an atypical migraine.

God, it's ridiculous how much doctors just call things anxiety when they don't know what something is/don't want to figure it out. I have the same thing - head pressure on the left side of my head but only when I sit up or stand. Does yours get better when sitting or standing by any chance then get worse when you lay down?

Same here! I also have TMJ and find myself clenching my jaw which adds tension to my neck which in turn gives me a headache.

I agree with the previous suggestion of potential migraine. This can relate to stress but can also exist and get better or worse on it's own.