Hello,
I cannot confirm anything without examination but it can be due to contact dermatitis to the material of the socks. Use a mild cleanser with moisturizing properties like Cetaphil. Also use cotton clothes and change the socks twice if there is any increased sweating
as far as possible. If the symptoms still persist then you can apply mild steroid like dermacort. For the itching antihistaminics like Benadryl or Claritin can be taken. If the symptoms persist then please get an evaluation done from a dermatologist.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your dermatologist. Treatment can be started only when the diagnosis is confirmed. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.