3277_,
Thank you for clarifying that for us. Looks like this may be expected behavior. If you are wearing your Apple Watch to bed, the alarm will sound on your Apple Watch. If you are in the Clock app on your iPhone, tap change, right under the Snooze option, you should see a message that says " When you wear your Apple Watch to bed, the alarm will go off on your watch".
You mentioned the alarm wasn't enough to wake you. Do you have the watch set to Silent Mode? Check out how to adjust your alert and notification volume here: Change the audio and notification settings on your Apple Watch.
You can submit feedback regarding this here: Product Feedback
Take care!