way one, u can try running lsof on mysql's pid pipe to "wc -l"
way two, ll /proc//fs/
these will give you the list of open file (including sockets etc, everything is a file in unix/linux)
open files limit can be check on the mysql-client using "show global varaibles like '%files%'" and then use "set global variable open_files_limit="
be careful about it, since the number from "ulimit -n" is total for the shell for all processes, and you dont want to put it too high.
if you see this number slowly increasing you ppbly want to check your code, there are dangling references...
hope that helps.