The skin on my hands feels hot, itchy, tight, and dry and my hands get red and swollen and become difficult to clench and unclench. this happens sometimes after i wash my hands. could this be an allergy to a type of soap?

Contact dermatitis shouldn't cause problem with moving your fingers. It is mainly manifested with rashes and itching so your hand symptoms are less likely due to soap-induced allergic dermatitis. Your description makes me think of a condition called erythromelalgia. You/your family member should take picture of your hands and show it to your doctor. A dermatologist visit is preferred. Good luck.