The outline on this picture is not uniform and I'm not sure how to fix it. I tried using the clone stamp tool but it's pretty hard having to rotate it to fix the outline. (I'm not even sure how to word this properly but I'll try showing it using the picture below):
Ideally by using vector shapes one can have exact borders. But that should be done from the start. To fix your existing drawing the current outline must be removed. Inserting a new outline as effect can create uniform result.
I made a selection and deleted the background and your outline:
I had to partially redraw the edge to make it smooth and sharp. It was done by pushing the black color against the selection with the smudge tool.
For a start the resolution was also lifted for sharpness, because I had only the low resolution screenshot from the question.
I inserted new background to a new layer. Then I inserted the outline as layer style "Outer Glow" to the original shape.