I'm trying to fix the inner and outer edges to this outline to make it look cleaner. What tools could I use to do this? I've tried using the brush and eraser tools and just haven't been content with what I'm able to do. Any tips would be greatly appreciated!
Alternatively, you could just use the Magic Wand tool to select the inner white space (or outer then invert your selection 'select>inverse') and right click the selection to 'layer via cut' the shape onto a new layer. Then add a stroke (layer>layer style>stroke) to the element.
If your image has some unseen color anomalies and you're getting weird selections try fiddling with the Magic Wand tolerance.