The only way someone can use your data is if they have cloned your SIM, which is insanely unlikely unless you happen to be a famous, infamous, or suspicious person. Or if you have a shared data plan which, as (I'm assuming) you are the person paying the bill, you'd know.
As for reading your text messages, that's a whole new ball of yarn. There are pieces of mobile malware out there, common for both iPhone and Android, which can do this. If you happen to have a parentally supervised account on iPhone, I believe that the person who is "parent" can check this. Many BYOD (bring your own device) companies have software that they put on devices to monitor them that give a shocking amount of access. Simply put, someone could be accessing your device many ways. The best way to mitigate this is to use a lock (fingerprint, passcode) on your device, and to only allow people you know and trust to use it. If you believe it may be happening, then do a factory reset, only install apps from the App Store/Play Store, and use a screen lock with a NEW password or a fingerprint (no 4-digit code, it's weak).