Would surface fill be a good option? If so, how do I use it?
1. Check your sketch. There are at least two points floating in space that are not attached to the spline.
2. The trouble here is that only the perimeter of the shape is defined. SolidWorks can "fill" the space in the middle, but it may not be the result you are looking for. Additional information (guide curves) are needed to help control the interior.
3. If you can reduce the number of points in the spline, it should help produce a better surface. I'm not sure what the end goal is, but fewer spline points are usually better.
The fill command did not like your original spline. I inserted a new composite curve and just selected your spline as the input. After that the fill command worked fine, but I doubt the results are very useful.
AttachmentsPart1.x_t, 143 KB
After remove those 2 points as Fredwsug telle you, add a sketch of a point in a new plan and sweep your sketch to this point.