My whole body has been itchy for a couple months now. I have no allergies. What could cause this?

See below. It's possible that you have dry skin, in which case using hypoallergenic skin cleanser and frequent hypoallergenic lotion applications should help. If this doesn't, please see your doctor soon for evaluation, because there's a long list of conditions that can cause generalized itching, and some of them need specific testing and treatment. Feel better!
Many things. There are a wide variety of things that can cause global itching. You should see your doctor and have some simple blood tests like a blood count, standard chemistries, and maybe a thyroid test.
Broad. Pruritis, or being itchy, can be caused numerous entities. Some can be rather benign and some can be very serious. If pruritis has persisted for weeks on end see a physician for a thorough evaluation.