If I load a kernel module and list the loaded modules with lsmod, I can get the \"use count\" of the module (number of other modules with a reference to the mod
It says on the Linux Kernel Module Programming Guide that the use count of a module is controlled by the functions try_module_get and module_put. Perhaps you can find where these functions are called for your module.
More info: https://www.kernel.org/doc/htmldocs/kernel-hacking/routines-module-use-counters.html