This can be a tricky one to pin down. Consider the ingredients in your current shampoo, conditioner, body wash and even as far as to what you wash your laundry in.
You seem to be using a good laundry product, which is mainly bicarbonate of soda. Your current hair washing product and shower gel may be harboring the culprit. People with sensitive skin may react to sodium laureth sulfate or sulphates in general as these are chemical foaming agents which are known skin irritants. You may find that dry skin is the cause of your irritated and itchy skin, so products that contain moisturising ingredients could be of benefit.
I’m going to recommend three hair and body products that are SLS free. They also contain less chemical irritating ingredients all round. Try some of these for a couple of weeks and see how your skin responds.
SLS free Shampoo:
SLS free Conditioner:
SLS free body products: