My Custom Skin won't Change

Here are eight possible reasons why your skin isn't showing:

1. Your skin has not refreshed yet. (If you're playing Minecraft 1.7 or above)
2. You never had a skin prior to the UUID update, which changes the way skins are stored (If you're playing any versions prior to 1.7)
3. You're not using a legal version of Minecraft, and therefore - Your skin isn't registered to your account.
4. The server you're playing on has online-mode=false. (Set to offline mode; no authentication)
5. You changed your char.png file within the minecraft.jar and not uploaded it to your minecraft profile.
6. You've uploaded it to your http://minecraft.net profile, but it's the WRONG dimensions (bigger than 64x64 pixels)
7. You're playing in offline mode.
8. None of youse have an internet connection.
9. You may have a bad internet connection and thus timed out or received incomplete information.

For #1, you'll just have to wait, and/or restart your game.
For #2, there's nothing you can do.
For #3, buy the game!
For #4, you should consider playing on servers that only allow 'premium'/paid users.
For #5, you should probabally log into http://minecraft.net.
For #6, you'll have to scale it down. Sorry :/ Unless you get the HD skins mod.
For #7, go online!!! (Same goes for your brothers)
For #8, you'll need to be connected to the internet in order to retrieve skins.
For #9, nothing I can say apart from the generic "get better internet" or "clear off your bandwidth by downloading/uploading less (ie. Stop watching YouTube on 4K whilst others are gaming)".

Very likely, based on the information you've stated that your problem is #3.

Skins can take time to do the initial trickle down. We (myself and the people I play with on a daily basis) have seen it take over an hour for everyone, including the person in question, to see the updated skin (people could see my Dr Who skin about 20min and 2 relogs before I could!!! Was frustrating :)).

You have done the steps correctly from what you stated in your post. As long as it said the upload is successful, all you should have to do now is wait.

Are you completely positive you restarted your Minecraft or opened a new launcher? In order to see your custom skin, you must successfully exit and restart your whole Minecraft.

Minecraft skins occasionally take a lot of time to upload and change; just be patient or check later by restarting.

Sometimes, the Minecraft Skin server is simply down or not working - check the status of all servers here

Sometimes it just needs time to upload - usually from 1 - 20 minutes so just wait. You could try all logging off then logging back on after a bit.