| it helps to look at what other people do. you can also do more with the chords. Instead of playing block (like strumming on guitar) play them broken (like pick-style). You can also invert them (don't have the root on the bottom, start on the 3rd or 5th) etc.
The easiest 3 chords to make a song out of are the tonic, subdominant, and dominant 7th.
you don't have to play notes that are only in the D major chord. The D major chord however has to be the foundation, and add the effect you want to the melody.
For instance, you can put one chord against another, like try playing an A major in the left and E major in the right. Gives a sense of dissonance, and you can resolve it to whatever you want. You do not have to be strict about keys...for instance bach switched keys numerous times in the middle of his pieces without even changing the key signature. Music isn't all about resolve and sticking with basic chords. Dissonance adds flavor, tension, and when you finally resolve to the tonic at the end of the song, it provides a sense of relief, and that sense of resolve lets the audience know it's over. for instance, would you stay on the V7 all the time at the end of a song? More often than not this dissonant chord is resolved back to the I.
oh and it depends what your job is what you do with the right. If you're a soloist, go ahead with the melody. If you're doing accompaniment, you can have a tertiary melody that complements the first (counterpoint) using things such as contrary motion scales (say you start on C, go through C major scale UP in right hand and down in left hand), parallel motion, etc. If you're backup, chords don't hurt. Make it fun! | 
