I have been playing the piano for a few years...not long.

[JDPriestly]

5. Couple of ideas. Try singing in harmony.

That gives you a sense of a part of each chord that is not in the melody.

Second idea, and I did this when I was in music school. Make flash cards for yourself so that when you hear the name of a chord, you automatically know all the notes in the chord. Say A major --- A, C sharp, E. Then add the minor seventh, G, the major seventh G sharp.

Practice playing lots of scales and the I, IV and V chords in each key. When those become automatic so that you don't have to think about them, you can focus on hearing the other notes.

Also, remember that often, the ninths, tenths, etc. -- those notes that are added to the basic chord structure, are really either part of the melody or connecting idioms that you can use to glue the music together. In a lot of music, the riffs the musicians who originally recorded or performed the song are so memorable that you will hear those fragments as you play the melody.