Well if your using 1.10 make sure its a 1.10 skin, I had that issue when I was using 1.8 trying to use a skin for 1.9
I am not an expert on this, but I was trying to use a skin made for 1.9 on 1.8.I don't know about 1.7-1.8 but try signing into your mc acct again.
You need to exit out of Minecraft completely for skin changes to take effect on Single player worlds.