What could it be my hands are swollen and they itch

Unfortunatly . Unfortunatly not enough information to give a good answer. There are many possibilities.
It . It is difficult to tell without knowing the duration of the swelling and appearance. Some of the options would include angioedema, urticaria, and contact or irritant dermatitis.
Swelling . Swelling and itchiness of the skin of the hands is commonly associated with allergic reactions. These type of symptoms are very stereotypical of the release by the body of histamine which is the major chemical involved in allergic reactions. However, depending on the length of time that your hands have been swollen and itchy for, the exposure of your hands to certain materials (soaps, detergents, iodine, metals, household chemicals, ingestion of certain medications such as antibiotics (penicillin and sulfa drugs), nonsteroidal anti-inflammatory drugs (nsaids), and blood pressure medicines (ace inhibitors), exposure to certain foodssuch as berries, shellfish, fish, nuts, eggs, milk, and others, petting certain animals, insect stings or bites), accompanying other symptoms like burning stinging or numbness that are more likely with a condition called angioedema, there may be other causes than allergies. Less commonly, your symptoms may occur in relation to inflammatory conditions, viral illnesses, autoimmune disorders such as lupus, and seldom leukemia and lymphoma. A form of angioedema may run in families and has different triggers, complications, and treatments. This is called hereditary angioedema. Your first mode of action is to try an antihistamine like Benadryl (diphenhydramine) or Claritin to see if it clears up but you should seek the help of an allergist in order to determine the cause of the swelling and itchiness in order to avoid a repeat of your complaints.