If the inflammation is spreading across your body, it might be ER time. Full body psoriasis (which is a rare thing but definitely a thing) is life threatening. The good news is that it can be treated. It's messy, but it works.
You've gotten some good suggestions about coal tar and some shampoos. Here's a list of best shampoos according to your symptoms: https://www.healthline.com/health/psoriasis/best-shampoo-for-scalp-psoriasis#A-quick-look-at-the-best-shampoos-for-scalp-psoriasis You can use a dab of shampoo as body wash if you find one that's soothing.
For patches on your body, you can't beat Aveeno baths for decreasing the itching and other discomfort.
This all assumes you've been diagnosed with psoriasis in the past. If not, it's doctor time.
For one thing, it could be ringworm, which isn't a ring or a worm, it's a fungal infection and it spreads like crazy. https://health.clevelandclinic.org/psoriasis-vs-ringworm/ Severe cases require medical treatment.
I know you don't want to go to a doctor, but make that appointment. There are other conditions that mimic psoriasis and you'll want to know which one you have plus get the best treatment for it.
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