Can you switch your apple ID on your iPhone without losing any data stored on your phone?

Let’s discuss the meaning of “switch my iPhone's Apple ID account to a different Apple ID account”.

This may mean two very different things:

1. Change your Apple ID. Perhaps you changed email service provider, for example, and you are planning to change your Apple ID. It will still belong to you. Change your Apple ID - Apple Support
2. Change the owner of this iPhone. In this case, some other person (or perhaps you with a shifted identity, such as personal vs. professional) is going to take over the iPhone.

In scenario 1, you remain the owner of the iPhone as well as all data stored on it. In scenario 2, expect to lose all data. In fact, you should go through this process when making the change:

What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

Leo__o wrote:

I am currently signed in using my family's "Apple ID" on my iPhone.

You should stop doing this immediately. Each person, regardless of age, needs her/his own, unique Apple ID.

The people acquiring new IDs need to thoroughly cleanse their Apple device(s) as follows before “moving in” using the new ID.

What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

This may well apply.

Set up Family Sharing - Apple Support

More info, basically repeating what is already above:

Make sure that each family member has a unique Apple ID - Apple Support