Sorry to hear that your getting device limited reached through Firefox.
Is this when you use TV Anywhere or through Sky Sports?
If you go to your account, on the right you will see My Profile under here you will see Device Settings and Sky Movies & Sky Sports. Under device settings this will show your devices registered for TV Anywhere. Sky Movies & Sky Sports will show devices registered for Sky apps.
Check to see if your device is within one of these sections that you would like to use. If it is not then try to stream a channel through either TV Anywhere or Sky Sports and this should prompt for registration. If it is showing as registered then as you have a device change, remove the device and re-register it. This will then work.
When I checked your account earlier there was one device change available, it is still showing that one device change. So the removal you tried through your account didn't work as there would be no device changes left.
Try it one more time to see if this time it will go through.
Make sure you go to My Profile > Device Settings > then remove the PC.