Try to connect your song's lyrics and structure to the overarching story that you're trying to tell. A lot of people put a lot of effort into the notes and tone of each line in the song, but if you think about singers that tell amazing stories, like Bob Dylan, they don't always have the best voice. It's more about the larger feeling being generated by the music. It also helps to practice. If you can keep your training in the back of your mind and just enjoy singing the song, you're more likely to live in the moment and bring some personality to your music.