Hi Arna16,
You can set an alarm on your phone and not push it to your watch. You can do that by going to the Watch app on your iPhone > Clock, and you can deselect Push Alerts from iPhone. But there currently is no way to do this the other way around. However, timers typically will not go off audibly on your phone when your watch is on and unlocked. Are you having an issue with operating it this way? If so, please let us know which iPhone you're paired with, the iOS version it's running, and your watchOS version. This will give us a better idea of what you're working with and how we can help.
We look forward to hearing back from you. In the meantime here's a resource that might be helpful: Add an alarm on Apple Watch
Take care.