I have never had eczema, but I do have some suggestions as a friend of mine also suffered from this.
If possible since you are a hairdresser, try wearing vinyl gloves when you wash hair and avoid using hot water, instead wash with cool to avoid further irritation and inflammation. Also try and keep hand washing to a minimum, and keep water temperature luke warm when you do.
Try applying moisturizers after washing, ointments that are clear and sticky seem to work the best but may not be practical, so maybe try using a skin protectant with petrolatum or silicone, ie Vaseline or Prevex. Try putting your hands in Vaseline and wearing spa gloves at night while you're watching TV or something? This might help the irritation. My friend also found Emu oil to work wonders, it's one of the mildest around and will help soothe cuts and cracks in the skin. If you apply this stuff consistently, you should notice a huge difference.
If nothing seems to be working for you, I would suggest seeing a derm specialist for perhaps prescription products to help with your discomfort.
Good luck hun!