Sore arms when I bicycle?
Since we do not know the specifics, I’ll take a guess and I’ll come up with a few hypothetical scenarios.
When road cycling, in particular, you may be collapsing your chest, dropping your heavier than normal in this position head (plus helmet) forward. Suggestions: shoulders back, widen chest area, position your head where it feels centered on your body, slightly tucked rather than extended.
Another possibility, esp. with road cycling, is that you cause the pain from your palms up. Try to avoid resting your hands on the handlebar in the little valley (heel of palm the area between the two bumps) where many nerves run. Sometimes that can be exaggerated with the use of padded gloves, when the actual padding causes extra pressure in that valley. Watch your forearm and wrist alignment too. One more thought: your saddle angle. If it’s too low in front, it will pitch you forward. Soften your elbows. Finally, if you’re referring only to mountain biking, I’m going to guess that it’s the downhill that aggravates your pain. You may need to take breaks. Soften your elbows, and try to distribute the weight throughout your body, stand on your pedals; the steeper the hill, the more you should shift your weight back. Enjoy your rides!