My hands hurt, and it's hard to make a fist, what could cause this?

Many causes: Many possibilities, cannot to say what is going on without seeing your hands and evaluating. Difficulty making a fist could be arthritis or inflammation in the joints, or irritation/inflammation in the tendons on the back of the hand, or stress injury on the hand, or infection of the skin, and more.

Hands hurting: Is there any history of injury? Chronic strain or overuse? Any swelling? Any redness or tenderness? Is the discomfort localized to the joints or does it involve the entire hand? These are important questions or answers needed to make a diagnosis. If symptoms persist, you will have to see your physician for evaluation.