What causes redness and swelling, tingling, burning, and itching in my hand?

HAND ITCH. Only one hand? How long had it been. It could be something you are in contact with. New soap? Work materials? Gloves? Hobbies? Be a detective. Do you take any oral medications?
Multiple. Start from local allergy, dermatitis, problem with nerves, arteries, connective tissue disorder, etc. Let your doctor find out.