Wearing shoes, which covers both the top of the feet like boots and also wearing socks in the state of Ihram is not permitted, even if they cover the shank or not. But if they cover a part of top of the feet, like straps of sandals and shoes (that a part of the top of the feet are shown by wearing them) are permitted. This ruling is exclusive for men and wearing socks and shoes has no problem for women.
If the towel of Ihram is long and covers the top of the foot, or the pilgrim for example puts a hot towel on the foot for reducing the pain, then these have no problem.
Whenever a man wears socks or shoes in the case of necessity or deliberately, this act has no atonement and obligatory precaution is to shear the topside of the shoe if the pilgrim forced to wear socks or shoes.