Select my own ringtone on Samsung s7 but only Sound picker is available
All you have to do, is clear defaults for the sound picker app. To do so, go to settings &rarr; application manager (apps) &rarr; in the three dots menu, select "show system apps" &rarr; sound picker &rarr; defaults &rarr; clear defaults. 

After clearing defaults, you will now be able to choose between the other options.

Oh and usually even within the sound picker you should be able to scroll all the way down, and it will have an option to choose a track from your phone.