Jesus, people, he's trying to learn something new. Music is worth learning and skills and knowledge are worth the effort to acquire. Is it so difficult to give a straight answer to a simple question?
I am learning my modes and now I am looking to start using them in my playing mainly for fills and riffs.
My question is about choosing what mode to use over a given chord.
For example say I am in the key of C and the Am chord is playing. I – vi – IV – V (C – Am – F – G)
I definitely know that I can use A aeolian but could I also use A dorian or A phrygian over the Am chord? They all have the chord tones in Am but I am not sure if you can choose a mode from a different key like A dorian or A phrygian?
The short answer is yes, you can. The chord tones in A minor (just the triad) are A, C, and E, and since all of the minor modes (dorian, aeolian, phrygian) contain those notes, they are all fair game. You may consider using the non-chord tones as passing tones in this case.
The slightly longer answer - yes, you can, but be aware that dwelling on the non-chord tones can imply a different chord. (For example - if you dwell on the F note in A aeolian while an A minor triad is playing, the implied chord is actually an F major 7th - but if you do that with an F# from A dorian, you imply an F# half diminished chord. The register in which you play the note will determine the inversion of the chord.) This is okay to do if you use your ears and know how/when to do it.
An addition to the slightly longer answer - as you begin to encounter chords with more than three notes (tetrads, pentads), you'll begin to find that the number of "correct" modes to choose from starts to get smaller. To use the example above, F major 7th (let's use the first inversion - so instead of ordering it F, A, C, E, we have A, C, E, F, also known as an A minor 6th) has four notes - A aeolian and A phrygian share the same chord tones, but A dorian does not due to the F#. It's something to think about once you get to that point.
The TL

R answer to your original question: Yes. You are correct. If a mode contains the chord tones, go wild.
Good luck!