Hi Charonn,
It sounds like you have an Apple Watch and iPhone that have a Bedtime routine set up, but the alarm goes off on both devices. We'll do our best to assist, so you can enjoying waking up more calmly.
The alarm should sound on both the iPhone and Apple Watch, if the Apple Watch is on your wrist. However, it should disable the other device when you dismiss the alarm.
Make sure both devices are running the latest iOS 14 update (after backing up anything important): Update your iPhone, iPad, or iPod touch and Update your Apple Watch
Disable Airplane mode, to ensure they are connected in Bluetooth. Avoiding any issues with the other device disabling the alarm.
Bedtime is set up on your iPhone. Make sure you have the right settings for this feature using these steps: Use Bedtime to track your sleep on your iPhone
To track that sleep on the Apple Watch, these settings can be found in the Sleep app and it's settings: Track your sleep with Apple Watch
If it continues, we'd recommend to Contact Apple Support
We hope this helps out, take care!