Could you give your opinion about my eczema on the fingertips?

Hi doctor,

I am a 23 year old female who has developed dry fingertips. The skin flakes off to leave smooth raw skin that has pins and needles when touched. It started with the index finger of my left hand. I asked a pharmacist for an opinion, and he thought it was nerve damage and recommended steroid cream. Over the last six months, it has spread to fingers of both hands. During this period, I also developed an itchy rash on the inside of my elbows. When I went to the doctor, she said it as eczema and prescribed me Dermol, Doublebase cream, and steroid cream. My fingers have not improved over the past month, but my arms have. Could you please give me your opinion on the supposed eczema on my fingertips? I am not convinced on what it is. Thank you.