Fix wobbly storage shelf
Most things we build are rectangular, and rectangular structures are prone to racking, which is illustrated in this drawing of a deck, but the same problem affects your rectangular shelves:  



As you see a structure can collapse due to racking if the joints flex without tearing apart.  

There are various ways to counter racking.  Other shapes, like triangles and trapezoids, are not prone to racking.  In the picture, by adding knee braces, you attach the rectangle to triangles, which are not prone to racking.  

Another way is to make joints that are not as flexible, it looks like the vertical boards in the front of your shelf are attached in a way that won't flex and allow your shelf to rack left to right.  

Another way to prevent racking is to attach a sheet over the rectangle.  For example, if you attached plywood over the sides of your shelf unit, there's no way it could rack front to back.  The sheathing doesn't have to cover the whole side.  You could add gussets - just a triangle of plywood in the four corners - and make the shelf nice and solid.