If your bike is well fitted but you are still having pain, take a look at how you are holding the bars. Consciously relax your hands, soften your elbows and drop your shoulders, and try to avoid gripping the bars too tightly. Your wrists should be relaxed and not overly flexed or extended.
Change your hand position frequently during a ride using the tops of the bars, the hoods and the drops, as each of these aligns your wrist slightly differently. Anatomic bars offer a wide variety of hand positions; some people enjoy the flat tops of wing-shaped aero bars, but others with small hands may prefer the more traditional narrow bar. It is worth experimenting to see what suits you.
If you have small hands, make sure your levers are angled so that you can cover them without strain; it may be necessary to use a shim or insert to bring the ends of the levers closer to the bar. This will also give you more control on descents.
Gloves are part of your protective kit and should always be worn to prevent gravel rash to your palms in the event of a fall, but padded gloves can also help to alleviate wrist pain. Padding around the base of the thumb can help take pressure off your ulnar never and prevent soreness.
Padded bar tape with gel or foam inserts underneath can give added protection from road vibration, another contributing factor in hand pain.