Hi wesley89631, I have similar symptoms after contact with detergents. In my case, the skin around the knuckles is affected the most (cracks and might bleed when bending the fingers).
If at all possible, try to avoid any contact with substances you are sensitive to. I would recommend a cream called Calmurid (or the alternative Udrate). It is a cream containing 10% Urea and 5% Lactic Acid. It is applied in a thick layer and left for a few minutes before gently rubbing it in. I have to say, it stings initially when you apply it to cracked skin but then the skin calms down. The combination of urea and lactic acid helps the skin retain moisture. Usually, cracks start to close within a few days but even after a day it already feels better.
If you are applying steroids or other medicated creams at the same time it is best to inform your dermatologist or GP. Your doctor will advise if you need to reduce your daily dose of steroid cream.