Hi Jessie!
Ditto what new12soap said.
If you just made the soap today, then what your friend experienced is actually what is to be expected. Soap will not be safe to touch (or wash)with bare hands until the lye reaction is complete, which can take up to 72 hours or so, depending on if the soap gelled or not. Before that, the lye is still very active.
As long as you are using 100% pure sodium hydroxide with no added ingredients (such as what is found in some drain cleaners), then there should be no problem with the lye.
For what its worth, there's no such thing as different kinds of lye for different kinds of skin conditions. The lye used for soap should say on the label "100% sodium hydroxide" (used for making hard soap), or "100% potassium hydroxide" (used for making soft or liquid soaps). If it lists any other ingredients, don't use it for making soap.
Soap needs to test out lye-neutral before using. Wait about 72 hours and then apply the zap test to check for unreacted lye. If it tests out neutral, it is safe to use, but still needs to cure in order to come to full maturity where it will be more mild to the skin, harder, longer-lasting, and bubblier. I let mine cure for at least 4 weeks before I even think of washing with it.
Always use gloves when cleaning up after making soap (and during making soap, too, of course), even if you don't have psoriasis, and especially if you do!
IrishLass