eczema

My oldest boy is 4 years old and has always suffered from eczema he gets constant skin infections we have been to the Drs multiple times who have just given us creams after creams. We have given regular bleach baths and used soap substitutes and nothing seems to work. I am at my wits end. We live in New Zealand and the Drs here are very reluctant to send for allergy testing and we can't afford to go private. He has probiotics and multi vitamins daily. My question is does anybody have any advice, know any