My iPhone photos
Is there a way to just have my photos on my iPhone and not my families photos and still have my photos save directly to the iCloud that my family shares?
Are you and other family members sharing the same Apple ID? If you are, you ALL need your own Apple ID. You can use Family Share to share content such as photos, apps, iCloud storage, music, etc., but first you all need to stop sharing the same Apple ID.
This link explains Family Sharing --> https://www.apple.com/family-sharing/