Hi obriencedar,
If you are trying to sign out of your Apple ID but keep contacts and photos on the device, you will be prompted with a question to "Keep on my iPhone" or "Delete from my iPhone". If you keep it on the iPhone, the content will download and remain on the device after signing out. Review "What happens when you sign out of iCloud on your device" in Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac to learn more.
Any downloaded apps under your Apple ID should be offloaded and redownloaded under the correct Apple ID. This way the app has the correct credentials when updating. You can offload apps by going to Settings > General > iPhone Storage > [App] > Offload. Then return to the App Store to redownload the app.
For more information on using unique Apple ID's and how to share content between family members, check out Make sure that each family member has a unique Apple ID.
Hope this helps.
Take care.