Hi there, nikkinicole314.
It sounds like you're having some difficulty with notifications when it comes to receiving text messages. We can help.
You've done some great steps in ruling some more common possibilities out, but we'll want to make sure we cover a few others. For instance, it isn't clear if Messages is the only app you're not recieving notifications with, or which version of iOS you have installed.
You can check out Update your iPhone, iPad, or iPod touch to make sure you are on the current publicly available version of iOS. If you're using a beta version of iOS, you can follow How to uninstall iOS beta software to get back on a publicly available version.
If you're finding this is happening on multiple apps, be sure that they are all up to date. If automatic updates isn't enabled, you can follow How to manually update apps on your Apple device instead.
Also, you'll want to make sure the issue with the notifications isn't due to the network you're using. If you're using a VPN, turn it off and see if there is any improvement, and see if there is any change in different locations for SMS, and different Wi-Fi networks for iMessages.
Take care.