If you have an Apple Watch connected to your iPhone, where you see the notifications will depend on which device is locked. If your phone is locked, the notifications will come to the watch, not the phone. If the watch is locked, they will come to the phone. If both are locked, they will also appear/sound on the phone.
The only way to get notifications on both devices if the phone is locked is to turn off wrist detection in the Watch app on your phone. However, this means you won't be able to use Apple Pay from your phone and that you'll have to enter a passcode to do much more than check the time.
If you're not getting notifications either place, I'd check Settings>Do Not Disturb. And, check that you don't have your watch on mute.