If my iPhone was on my family's apple ID, and I want to switch it to my personal ID, will I lose all of my photos/contacts/etc?

It depends where the data is stored.

If it stored locally on the iPhone you will be able to keep it when switching the Apple account that is logged on to the iPhone.

If it is stored in iCloud you will need to first disable iCloud for the current account logged onto the iPhone and create a local copy of the iCloud data (iOS will ask you if you want to keep the data on your phone when disabling iCloud, say yes).

See if the below helps.

When changing to the new ID, there may be some data loss, but you can minimize it. If syncing photos with iCloud, ensure Optimization is turned off in Settings/Your Name/iCloud/Photos and/or in Photos/Preferences/iCloud. Then make sure full resolution photos are on the device/computer. When signing out of iCloud, if asked whether you want to retain data, choose yes. Messages conversations will be lost if they are addressed to the ID. See the article below for other places that the old ID should be removed. See Winston Churchill's response in the below discussion. If possible, also set up Family Sharing  between the IDs to keep access to your apps/purchases. 

 How to switch Apple IDs on your iPhone or iPad.      

How to transfer all files from one iCloud account to another.       

What to do after you change your Apple ID or password - Apple Support.      

Family Sharing.         

Family Sharing - Set up.