He seems to be having Hives/Urticaria. Urticaria presents as skin welts, which can be distributed all over the body. Itching is usually present.
Acute Urticaria OR hives can occur due to various causes; common causes that can cause urticaria are...
Thank for asking to HCM
I really appreciate your concern the given history suggested the hypersensitivity reaction due to the drug called "Allopurinol" in very rare case this drug induces the reaction but the eruption of rash goes away as soon as you stop taking the drug and nothing to worry...
Diagnoisis of rash involves thorough clinical examination, would sugest you to send us clinical photograph for further assesment.
If the rash is not associated with other symptoms then there should be no cause for concern.
Apparently, you are using the medicine and the soap for quite some time - less likely to cause a new event like this
The distribution of your rash does not suggest a definite diagnosis
Psoriasis is diagnosed by seeing and/or at times scraping and blood tests. Your doctor is the best person to...