I am sorry to hear that your unable to use Sky Sports through your iPad nor iPhone due to error of device limited reached.
If you can sign into your account, under My Profile select Sky Movies & Sky Sports. This will show the devices registered for Sky apps, you should see the iPad and iPhone. For now if you can remove one of the devices either one, and remove the app. Then re-install the app, log in to Sky Sports on the device itself and start streaming a channel, this will prompt for registration.
Once this device you chose is working then we can do the same with the other device.
Sorry, but I'm afraid your advice didn't help, simply because the 'My Profile' option is not offered. All I have concerning my account when I log in is the "Gear Wheel" and that does not present any options on Sky Movies or Sky Sports.