Even if you can watch at home, doesn't mean you have the remote connection side of the slingbox set up properly. Certain apps require a TCP stream to connect to the slingbox remotely. If you haven't set up your router / slingbox correctly to work with a TCP stream, you won't be able to connect with a lot of mobile devices.
First thing you need to do is Sign into your sling account
Support will bring up your slingbox. If it hasn't been setup for remote viewing correctly you will see a warning sign. If that's the case, then you'll need to access your router and re-run the sling setup in order to provide port forwarding settings for your router
If that's not your problem, you'll need to provide more information in order for someone to try to help you.