SolidWorks has an add-in ScanTo3D, but with curve data you might not get far with that. Most people go from mesh (point cloud) data to surface.
There are also dedicated packages for reverse engineering (but they can be expensive), or if this is a one-off, hire a contractor to do it for you.
If I were doing this, I would use the curves as reference, and do surface/solid modeling around that. If you want something that looks really clean, that is your best option.
You can try and split border lines for main surfaces (bottom plane, sides, corners - as simple, as possible), delete the rest of the curves, create separate surfaces for each of the cells and then join them together. For some of these patches you will likely need additional curves (for example, to create round corners).
Check out Meshlab, it is free and can take many file types. I typically use it for reducing the number of surfaces in .stl files so that SW can open. The number of faces/surfaces limit for SW is 20,000. So I import into Meshlab then go to Filters->Remeshing, Simplification and Reconstruction-> Simplification: Quadratic Edge Collapse with Decimation and enter the target number of faces as 20,000. Then I save and open in SW, when opening make sure .stl file type is selected then click options and check the solid body option. That way you can go from an .stl straight to a solid body (as long as there are no holes in your surfaces).