C++ : N line segment Intersection
Depending on how long the lines are and what the likelihood of intersections is, you could also use a spatial join. I.e. you treat all all lines as rectangles, put them in a spatial index and search for each line with which other lines it overlaps. You can use a standard R-Tree or Quadtree, but I would actually suggest a PH-Tree here, for example this one, because they are very fast for window queries with small result sets (for example if you expect usually only 1 intersection). For all results, you would have to manually calculate whether the lines actually intersect or not, because overlapping rectangles is an indicator for overlap, but obviously not a guarantee.

Also 'Sweep Line' is more of a general approach of tackling a problem, a bit like 'divide and conquer'. It is not an algorithm in itself, you would have to be more specific how you would use it to solve your intersection problem.