Hard lump on right side of penis under the skin.

Need to examine: It is likely to be a sebaceous cyst, but you should see your doctor for a proper diagnosis and treatment.

Here are some ...: Is it movable? If so, most likely, it's a bump that is related with hyperactive sebaceous gland. If deep, check if you have a bent penis at that spot; if so, it may be related with Peyronie's disease. Clinically, "hard lump on right side of penis" is just like a conundrum to guess; without a direct look and palpation, it's still hard to be accurate. So, ask Doc timely as needed. Best wish ...