Extreme itching on feet and hands with no relief when scratched

I have no idea what is causing this insanely persistent itching on both feet (toes and tops) and my hands (mostly fingers and palms). I thought athletes foot at first- did all of the treatments for it even though there isn’t anything visibly on either my feet nor hands. Obviously not athletes foot. Went to emergency room and was given Zyrtec and an antibiotic two weeks ago. I get some, but very little and short term relief after taking the Zyrtec. Again nothing is visible on skin when the itching starts- once I scratch I can’t stop/ this causes redness and bumps. The itching is so bad I’ve caused myself to bleed. It truly feels like it’s coming from the inside of my body or something- not just surface level. No new soaps, metrications, etc. Please help - it’s driving me crazy and I can’t deal with the non stop extreme itching much longer. I’m miserable. Also hot water or heat make it burn and itch worse. Plus I have had excessive sweating this year, unexplained weight gain and had psoriasis for first time on scalp last winter. I’ve washed with a tea tree oil medicated wash and works will applied but not once I rinse off. The itchy spots do sometimes turn hard and dry.