I would recommend that, if these symptoms persist, you go to see your primary care doctor
who can take a look and help you figure out what is going on.
By far the most common cause of itchy feet is something to do with the skin. For example, fungal infections of the feet, called athlete's foot, are very common, and sometimes these can cause only minimal rash or redness, together with odor and itching. Your doctor can take a close look and make sure this is not going on; if so, it is usually easy to treat with simple topical anti fungal medications.
Another common cause of itching feet is excessive sweating of the feet, leading to irritation of the skin. This can be prevented by wearing cool, breathable socks and by paying good attention to foot hygiene and moisturizing.
Rarely, itching of the skin can be a sign of a serious internal problem, such as a problem with the liver or with the kidneys. Given that the itching is only on the feet, this seems unlikely, but your doctor will be able to help you decide whether or not basic blood work might be a good idea.