My psoriasis came on 3 years ago - with a vengeance! I did not know what it was, and doctors were clueless (and predictably incurious). It burned, stung, and oozed. The itching nearly drove me insane (or perhaps it succeeded - not sure - haha). The ONLY thing that calmed the burning was coconut oil (extra virgin organic) but was not 100% effective. It sure helped, though.
For the itching, I discovered by accident that running the area under VERY hot water - almost scalding - was incredibly effective and the relief lasted for several hours (AH! Sweet sleep! ) but I had logistics problems because I could only access the bathtub faucet which prevented a lot of areas from getting this relief. You'll need to be right at the controls, as your skin will tell you "hotter" or "cooler" as needed, and it will vary by the moment. Pat dry w/ paper towel & don't apply anything to the skin.
There are a few theories why the hot water works, one of which is that it forces the release of histamines out through the skin. But as far as I know, no one really knows why. It just does.