Hi Kerry,
I'm obviously not a doctor, but I wonder if it's not the holding of the rod but the snapping action of the casting, that is the issue. So swapping rod hand may not solve the issue unless you change your casting action?
I sometimes get a bit of that tennis elbow type pain at the end of a week of fishing, usually at the moment I really snap a softbait cast forward.
I am right handed and have my left hand on the rod butt, and my right hand at the reel.
I wind right handed because that's the way I learned (dropping bait on an egg beater). I've contributed to this type of debate before, my view being that I'm so much more co-ordinated with my right hand for subtle winding to tighten the line on the drop etc, and I'm not that weak with my left that I can't fight a big fish adequately on softbait gear. Might be different game fishing or jigging for kingies etc.
Anyway, all the best. That type of niggle is miserable.
I do typing/hand writing/mouse use for my job, and years ago had burning ligament/muscle thing in my right pen and 'mouse' arm. I could feel the muscle on top of my forearm twitch every time I moved my finger and hours of that a day caused the issue.
My employer's response was to tell me to switch my mouse hand, rather than any physio etc. So I switched the mouse to my left hand, which felt unco as anything to start, but it soon got better. So I'm sure you'll be able to do the reel switch adequately in a short while and you'll be handling 18lbers on light string with no probs!