I agree that solfege is good to practice. It sounds like maybe you are having a difficult time playing and singing at the same time? Or are you also having trouble just singing the vocal line that you composed?
For the first issue you might try practicing both parts separately until you really have them down and them try them together slowly, bit by bit. You could also try recording one part and then playing or singing along to that. Another exercise might be to play block chords on every beat while singing the melody to get used to playing and singing at he same time.
If your melody is hard in general, maybe try and analyze it to make sure you know where the notes fit in the scale or chord. As for solfege, try practicing running up and down the scale on each scale degree and then up and down using different intervals. For example: do, re, mi, fa, so, la, ti, do, ti, la, so, fa, mi, re, do... Re, mi, fa, so, la, ti, do, re, do, ti, la, so, fa, mi, re... Mi, fa, etc... Then... Do, mi, so, mi, do... Re, fa, la, fa, re.... Etc...
Also, be careful about using the word counterpoint, since in classical music that refers to a specific set of rules usually associated with Baroque music.