I experienced a lot of hand pain and numbness on my Moots--a bike that was custom designed for me. I started off with an FSA bar that had a flat top. I hated them, and switched to the bars that are on my Bianchi--Deda 4 Girls. They have a smaller diameter and round top. My pain got slightly better but did not radically improve.
Utlimately, I came to the belief that the bike's geometry was just wrong. The reach was too short and the seat tube angle too steep (even with an offset seatpost) to get my weight rearward enough to take the weight off my hands. I worked with a biomechanics expert/fitter who just couldn't quite figure it out.
So, while I wouldn't discourage you from changing out your bars, I have to wonder whether there's something in your bike's set up or geometry that is the real issue--along with your own physical issues.
The pain and numbess I experienced has not completely gone away, despite the fact that I haven't ridden it in a year. I did permanent damage to the nerves in my hands. So, be carful pushing through this.
Live with intention. Walk to the edge. Listen hard. Practice wellness. Play with abandon. Laugh. Choose with no regret. Continue to learn. Appreciate your friends. Do what you love. Live as if this is all there is.
--Mary Anne Radmacher