There are two likely possibilities here. The first is that you could have a fungal infection of the foot, called athlete's foot, which causes itching, scaling, and redness. The fungus that causes athlete's foot can be picked up in many environments, including bathrooms and gyms. It thrives in skin that is moist and dark, such as the environment provided by feet inside of shoes! Part of treating foot fungus is therefore to keep the feet clean and dry, which sometimes means changing socks several times a day. Also an over the counter antifungal cream should help a lot, although sometimes more severe cases do need prescription medications.
The second likely possibility would be eczema
, which is a condition caused by dryness of the skin, which leads to itching and redness. Hydrocortisone cream should have help the eczema, which makes me lean more towards fungal infection, but sometimes more severe cases of eczema will not respond to an over the counter hydrocortisone cream.
I suggest getting in to see your primary care doctor
, as they will be able to diagnose precisely what is going on and help you decide what medications and other treatments are suited for your case.