Hi Ads!
Everyone is different, but I've found I develop the same sort of pain in the same area of my arms when I try to ride straight handlebars instead of my usual drops. I just seem to be one of those people whose hands have to generally face each other when riding in order to be comfortable.
Another data point: I found similar pain when I developed tennis elbow. It hurt in the same area when riding regardless of my hand orientation. Avoiding the sort of off-bike repetitive motion that caused the problem helped, as did wearing a brace while riding.
Pain of any sort is a general indicator of something wrong, and if you can correlate it with an activity, it is easier to address the root cause. Perhaps looking at the totality of bike fit will help. My father has one arm slightly shorter than the other after a shattering bone-break in his youth. He rode in pain till we figured the way to address it was to rotate the (quill) stem in the steerer so the handlebars didn't point straight ahead. The handlebars no longer point straight ahead...but the bike does, and he no longer hurts.
The "little things" sometimes make a very big difference indeed.
Best,
Dan.