Pain can be the result of a lot of different things. Most obvious is to much weight or pressure on the hands. To correct that a longer or shorter stem, or more or less rise may be in order. Also, a light(er) grip maybe all that is necessary. People also have a dominant hand. As a result they may over tense (or overuse) it without thinking about it or in some cases over tense the opposite hand to balance out. Also, your handlebars may need to be rotated slightly which may help.
Gloves might help or exacerbate the problem as well. Over padding can cause pressure points while less padding may not provide enough comfort.
Definitely get fitted. Tell them the problem you are experiencing and have them look at your posture while pedaling.