Change the pitch as the chord dictates. Keep things simple. Now change progressions to something new (perhaps C Bb F G), and improvise a new melody. If you find it hard to play and sing at the same time, try just playing for a minute or two, and then echo what you just did by singing.
What do you do if you can't write a song but sing?
It might be a good idea to try singing alone, without resting on your strength on your instrument. Snap your fingers, clap, or try writing the melody to a track you've already recorded. This way you are isolating your melody, and can focus on it to create something you love.