Is there any free software similar to CellDesigner that allows me to represent large networks of biochemical reactions in the human body?
Here is a list of such programs. It is an old post but most of the tools it lists appear to still be functional. I found this by just googling "celldesigner alternatives", which is always a good idea to search first for these things.

I have used cytoscape and it is ok, maybe too general also for your purposes. For very simple purposes I have used KEGG pathway in the past, which is in addition to the others.