My first 2015 submission was also art. ^^
The lines look like they were drawn with a mouse instead of a stylus. If you only have a mouse to draw with, I would suggest you turn on stroke smoothing to get smoother, more natural-looking curves. If you want to, you could also trace over a reference treble clef design on a separate layer.
I'll also complain that the color combination is very discomforting to me. Fortunately, if your program supports it, you can draw on different layers, then easily adjust the color of each layer until you find something you really like.
I don't know what features Paint.NET supports, but GIMP does everything I want it to do, and it's also free. I had a better experience with stroke smoothing in Photoshop, but it's too expensive.
Props for making your own logo, and I hope to see you work on it more! ^^