I have cellular data and notifications on but when I’m off the WiFi I don’t get any push notifications or text messages

There are a few things that could be going on. Depending on what you are expecting to get push notifications for, make sure that those apps are set to use cellular data. Text messages, at least true text messages, which as SMS, are a carrier function, and they rely on the cellular signal, not necessarily cellular data. If you can receive and make a phone all, you should be able to receive a text message, as long as your cellular account has SMS provisioned on it. If this is the case, you may need to check with your cellular provider. Also, check Settings>Notifications and then check the apps that you are expecting notifications from and make sure they are turned on.

If you are referring to iMessage, the blue text bubble, those rely on data. Cellular data would need to be on for messages. If you are away from the house and on cellular, can you do anything that requires the internet, such as using Safari?

What notification are you expecting a push from, and for iMessage, if you are not receiving them, check to make sure that cellular data is turned on for the Messages app, and see this support document for additional troubleshooting steps. If you can't send or receive messages on your iPhone, iPad, or iPod touch - Apple Support