If you're playing just chords then I'm assuming you or someone else is singing/playing the melody. This is also my preferred method. Chords in the left hand, especially when the third AND fifth is involved, can sound muddled to me, so I prefer to keep my left hand playing fifths, octaves, or sometimes a song can have a completely different note in the left hand (you might see a "C/E" or an "F/G" chord, which is something Elton John and Lionel Richie (and others) employ in some of their songs).

To get to the next level, you'll need to improve that left hand capability though. A couple songs that have helped me improve my left hand are "Don't Stop Believing" by Journey and "Great Balls of Fire" by Jerry Lee Lewis because those songs without a solid baseline are horrible. Here's a good tutorial for Great Balls of Fire (https://www.youtube.com/watch?v=w5mVylL3GXw).

Keep it up! Being able to play songs that I enjoy from church and the radio have been life savers for me. Let us know how it goes.