Have you tried starting your phone in Safe Mode to see if the mobile data works? If not, please give this a go by holding the Power button > Hold onto the Power off icon > Tap Safe Mode when prompted. This mode will temporarily disable most third party apps and allow your phone to run on its most basic interface. If the issue does not persist in Safe Mode, it points to the issue being caused by a third-party app, and so I'd recommend deleting the apps one by one until you find your culprit.
And, before I forget! You can exit Safe Mode by restarting your phone.