Other than to agree with your doctor about the eczema business theres nothing really I can say on the matter, except one of my girlfriends, who sufferes eczema uses a aromatherapy remedy. and she swears by it.
sooo, if you can be bothered: 10 drops chamomile german 5 drops yarrow 5 drops tagetes
dilutd in 30 ml vegetable oil, 30 drobs jojoba oil, 10 drops evening primrose oil
unlikely, I know, but If you have any aromatherapy shops near you they'd prolly knock it up for a couple of quid.