My DD was the same from 10 months, SCREAMED and cried until she got the shoes off. Socks were as much as a problem as shoes. This eventually turned into a clothes thing too.
For almost 5 years I treated it as a tantrum and yelled and smacked her when she wouldn't get dressed or leave clothes on or wear certain shoes and socks. She would cry and say it hurts it hurts it hurts. I said there is no way in hell it can hurt you, its a sock.
Well, finally at the age of 5 DD was diagnosed with Sensory Processing disorder - Tactile defensivness.
Basically, the feeling of certain things on her skin/feet etc actually sent her nervious system through the roof to the point she really couldn't tolerate the feel or sensation. With her it was partically socks, anything with lace, ribbon, 3/4 pants, frills etc and the biggest one was denim. She also hated hats, head bands, clips etc
She has gotten better with age, but at 6 its still almost impossible to get her to wear denim. In rare cases, there is more to it than just kids not wanting to wear shoes and socks. She is fine with shoes and socks now but she has to try them all on and find ones that 'feel right' to her.
PM me or email me if you want to know anything else about it!