On the right hand tingling and numb.
This, too, is my first summer riding and I've hand a problem all summer with my right arm and hand going numb and becoming painful not just on the bike.
I just discovered in the past couple of days that if I message the base of my neck on the right side that the numbness immediately goes away.
My point is that the problem may not be at your hands. Mine, I believe, is at the base of my neck.