You can quickly download and install the Straight Talk att.mvno APN (it's what allows your phone to use the cellular data network) by going to unlockit.co.nz from your iPhon.e. Just tap Create APN and choose Straight Talk.
It won't fix your MMS / picture messaging, though (unless you're sending a pic to someone with iMessage). For that you'd need to do the T-Mobile SIM card swap method to be able to access your phone's cellular data settings