I was responding to Alex and indirectly to fyip. But to me, you are a youngster also.
You are correct, the photos app will not let you delete them because they weren’t synced through iCloud. You need to connect the phone to your computer, then locate it in Finder (if you are using Catalina) or iTunes on older Macs and Windows. Click on it and, after a delay, you should see a Summary screen. Across the top will be things to view. Click on Photos. This will list all of the photo albums (as folders) that you synced from your computer to your phone. Uncheck the one(s) you want to get rid of, then click Sync or Apply in the lower right corner of the screen. (This is what Chris posted, but in more detail). If you don’t see any when you click on Photos post back with what you do see.