I tried to change skins now using minecraft.net and it worked.
Might have been something wrong with the website itself? The problem persisted for two days though.
I'm glad is back up and working properly!
Thank you for your time.
I'm slightly confused on why the Resolution Status was marked as invalid.
The method suggested by GreyVulpine at #minecrafthelp solved my issue.
If the issue was fixed, whatever it's origin was, this suggested method was a temporary way to fix my problem making me wonder why it was marked as invalid.
I changed my skin on the same day I posted this issue here and I didn't changed it since then.
Right now I'm not aware if this is still an issue.
This has been reported at the Soartex Fanver Forum as initial thought of being a Resource Pack issue. Here are the screenshots provided by the user http://imgur.com/a/vhF4n