>> What can I do to get rid of the shadows?
Unless you like flat portraits, shadows are okay to have as they give relief (3D) to the image. Problem in this case is that you're getting wonky shadows because your main light is not positioned/bounced properly (light is coming from low angle) and your reflector is not properly setup (too close perhaps, main light should be 2-3 times stronger than fill light).
Google "Rembrandt Lighting", "Broad Light" and "Short Light". These should be your starting points. It doesn't matter if you're using continuous lighting, direct or bouncing flashes, principles are the same.
Quick example below of a portrait I did with a white background (wall):