My mom 67 has swelling in her right leg and right hand with only pain in her hand?

Hmmm . . . now that's an interesting one.  Several reasons for swelling but usually it's either one leg or both; the arm(s) are rarely involved.  Heart failure, liver failure, and/or kidney failure affect the body equally on both sides such that if there's going to be any swelling, it should be symmetric on both sides of the body.

Right leg swelling alone can be post-traumatic, venous insufficiency, post-phlebetic, infectious, or due to an acute blood clot (which is very dangerous).  Right arm/hand swelling alone can be due to the above, too.  However, short of being involved in some trauma on the right side of the body, I can't imagine why you'd have swelling on both the upper & lower extremity on that side but not your left.  

Best to go see your family doc or geriatrician.  Good luck!