If you don't have a C compiler, then you are going to have a hard time solving this problem. Presumably, the operating system has a function that give the time with a higher accuracy than the Perl builtin time(). Calling the C API from Perl requires an XS module compiled by a C compiler.

The Time::HiRes module provides an interface to the gettimeofday function that will do the job. But you can't compile it because you don't have a C compiler. And can't install Perl modules.