I have a composition animation I downloaded and I can't change one without changing the other

You have to duplicate the correct precomposition and also the 'final' composition and any other intermediate composition. Then you will have to change the content of the correct precomposition so that it's change follows through the composition hierarchy you have duplicated - this ensures that other compositions that are connected to the 'correct' precomposition are not affected by content change(s).

As Rick suggested, look at the Comp Flowchart - begin by selecting the 'final' comp and selecting flowchart view or mini-flowchart view.

Alternatively, you can use Master Properties which precludes having to duplicate multiple precomps/comps. Go to the 'correct' comp and invoke the Essential Graphics Panel (EGP) - then name it appropriately. Then drag the SourceText property of the Text Layer(s) you want to edit, into the EGP. Go to the 'final' comp. Select the precomposition that contains the sourceText property you dropped into the EGP. Hit UU (letter u, twice; quickly) to display its Master Properties, in the Timeline. Right-click on the Source Text Property and select Edit Value to invoke the Text Entry box for Master Properties. Type in the new text and hit OK. Done! Takes a while but it should be quicker than creating multiple duplicates of all affected comps/precomps.

The Master Properties feature allows you to create versions of an original/source/master property without affecting the original. IOW, while a relationship exists between the Master/Source Property and its copy/clone, the copy/clone may be adjusted with variations of its characteristics/properties.

If you have intermediate comps between the 'correct' comp and 'final' comp, you will have to drag the sourceText property (or any other property you want to designate as a Master Property) from the 'correct' comp into the EGP of the intermediate comp. This ensures that the Master Property carries throught into the 'final' comp.