I have pain on top of my right hand between my thumb and index finger. Could there be a broken bone in there? That is what it feels like.

Arthritis. Unless you have fallen or had some significant traums to your hand it would be extremely unlikely that you have a broken bone. The joint at the base of the thumb in that area is the second most common site for arthritis. It affects women about six times as frequently as men -- and no it is not because they work harder -- but due to hormonal effects on the ligament causing them to be looser.
1st web space pain. If an injury, consider x-ray to check for possible bone injury.