Most hand/wrist/arm/neck/shoulder pain when bicycling is caused by poor posture on the bike. In particular, you are probably not bending your arms enough when riding. Locking your elbows almost always leads to hand/wrist/arm/neck/shoulder pain. You should always have a good bend in your elbows when riding.
If you have trouble riding with your arms bent, here are some things to try:
1. improve your core strength so you can hold your body steady with your core, not your arms
2. adjust your saddle - most beginners have their saddles much too high
3. bend more at the waist - road bikes are not designed to be ridden with a very upright body position