I sculpted this based on my beginner knowledge (forsaking any complex sculpting knowledge that might discourage and keep me from getting to the end), but now I want to paint and pose the character and I have a feeling this topology is going to be difficult to work with. Where do I start?
It might be worth it to try and install the new experimental blender 2.81 version and use it’s “voxer remeshing” feature. I don’t think it would fix everything instantly but it could give you a start. Keep in mind that it’s still experimental though so it might do what they intend it to do in the long run.
Heres one way of doing it, but It envolves recreating the topology.
Set the snapping mode to face. create a new mesh, and delete all except one vertice. press g and move the vertice, the vertice will automatically snap to your character mesh! now, extrude the vertice to create edges and faces, (using the poly to poly method of modeling) and whenever you extrude or move the vertice, it will snap to the mesh.
I realize this is time consuming, and I suggest you plan your topology flow with the grease pencil, setting the stroke placement to surface.
With your current mesh, I don't see any fixing it, I think this is the only way to get a mesh suitable for rigging.
hope this helps, and please comment if you need more detail.
P.S, I like your model, and It's really good for a beginner! I'm a beginner at sculpting too, and I'm not sure I could create that model.