Are you renting or buying? First check out the water hardness in your area. If buying get a water softener. If renting find out if they will let you install one.
I have a specific type of eczema that only affects my hands.
http://www.pompholyx.co.uk/When I lived in the US I controlled it by slapping on some extra moisturiser from CVS. Nothing fancy, maybe happened a few times a year no big deal. I didn't even realise it was eczema because I just figured weird dry skin thing. I never went to a doctor about it.
I moved here and my hands became so badly affected I was covered in itching sores fror months at a time.
In the US it affected one finger. Here it affected four on each hand. It became infected. I couldn't bend my fingers to type my shoelaces or hold a pen.
I went to the GP and she gave me a cream I had already bought over the counter. I went back the next week and saw some guy from the Czech Republic and he gave me antibiotics. I have been religiously using E45 hand wash for regular hand washing and body wash in the shower. (The rest of my body is fine, but the soap gets on your hands of course). Also, lots of lotion, enough to drown a horse.
I haven't had an attack since. Only a slight raise on the skin that I then attacked with extra lotion.
It is apparently, the water in the UK that causes the trouble and could be water in your area of the US. My area apparently doesn't even have water that is all that hard.
http://news.bbc.co.uk/1/hi/health/7820081.stmAll you can do is move and see. It can be affected by stress, so if it gets worse right away, give it a few weeks and see if it calms down. If it doesn't it could be the water.
The article states that 20% of UK children are affected. Most studies seem to suggest that 9% of US children are affected, but then the US has more immigrants and I would suspect that some races are less affected than others which might explain some of the difference.