This is happening because of two things.
Because you are using N-gons. N-gons perfectly fine when making hard surface models but when it comes on to topology, they get a bit difficult to work with.
You have faces on the inside of your model. This is a no no and the Edge Ring tool will detect these when you are trying to make a ring and won't allow it.
So to fix, you can use the Knife tool to try and cut the ngons into quads (See this post on how to use the Knife tool), don't just select vertices and press F. Next, remove all inner faces of your model, you can just go into Wireframe view and select the faces and use X > Faces.
Trying to create an edge ring with inside face(s).
Creating an edge ring without inside faces.
Trying to add edge rings to an Ngon vs trying to add edge rings to quads.