My DIY bookshelf wobbles badly despite using corner braces—what did I miss?

I built a simple wooden bookshelf from pine planks for my home office. To keep costs down, I skipped professional joinery and just screwed the shelves into the side panels. After noticing it wobbles quite a bit, I added corner braces on all four corners, but it still sways when I gently push it. The screws seem tight, and the braces are metal L-shaped ones from the hardware store. I want it steady enough to hold my heavy textbooks without tipping or shaking. I haven’t added a back panel yet, thinking the braces would be enough, but maybe that’s the problem? How important is a back panel for stability in these kinds of DIY shelves? Also, could the type or placement of the corner braces be causing this wobble? Any suggestions for reinforcing it without rebuilding from scratch?