Thanks for your query.
You seem to have developed a fungal infection
of the hand which can be either tinea
infection or candidiasis
You should try to keep the affected region clean and dry.
Do not apply any kind of oils or moisturizing creams over the affected region. You need to use an antifungal cream over the affected area.
Something like Clotrimazole
gel if very effective in such cases.
Also you might need to take oral antifungals for upto 6 weeks.
And to relieve the itching, take oral antihistamines like levocetrizine once a day .
Do not apply oil or any other creams over the affected area.
Hope it helps
Dr Geetika Paul