How to separate merged photo albums when sharing an Apple Account?

My guess is that you turned on iCloud Photos on both phones. They both synchronized against iCloud - each of them adding its photos to your iCloud Photos library, and pulling down copies of any other photos it found there (i.e., photos uploaded by the other phone).

Normally you would want to use iCloud Photos.

• If you use iCloud Photos, the master copies of your photos are stored in iCloud. If something happens to your phone ("gets run over by a truck"), you can access synchronized photos from any Web browser (by logging in to the Web site https://www.icloud.com/ ). You also get synchronization between devices, something that has been very convenient for me (photos on my iPhone show up in my Mac's main Photos library, and vice versa).
• If you make iCloud backups that include photos, you can't see what photos are in a backup without restoring that backup to a phone, wiping the contents of the phone in the process. And you might be copying all of the photos every time you make a backup, making backups take a lot longer.
• If you are not backing up your photos in either of these ways – but depending on manual imports using a USB cable, or worse, never backing up your photos at all, you risk losing them if anything happens to your phone.

But here it has done a one-way merge of your photo libraries … which is exactly what it is meant to do when you start synchronizing two different devices that both belong to you, but that have different photo libraries.

As long as you use the same Apple ID, you are likely to continue to run into problems with stuff being shared that you do not want to be shared.

You may not want to hear that answer, but it is the correct one. An Apple ID is meant to be for one person – and synchronization features are designed around that assumption.

As for separating your photos – you're going to have to do that manually, once you get the "same Apple ID" issue sorted out.