Is there an alternative sleep function in C to milliseconds?

Yes – older POSIX standards defined usleep(), so this is available on Linux:

int usleep(useconds_t usec);

DESCRIPTION

The usleep() function suspends execution of the calling thread for
(at least) usec microseconds. The sleep may be lengthened slightly by
any system activity or by the time spent processing the call or by the
granularity of system timers.

usleep() takes microseconds, so you will have to multiply the input by 1000 in order to sleep in milliseconds.

---

usleep() has since been deprecated and subsequently removed from POSIX; for new code, nanosleep() is preferred:

#include <time.h>

int nanosleep(const struct timespec *req, struct timespec *rem);

DESCRIPTION

nanosleep() suspends the execution of the calling thread until either at least the time specified in *req has elapsed, or the
delivery of a signal that triggers the invocation of a handler in the
calling thread or that terminates the process.

The structure timespec is used to specify intervals of time with nanosecond precision. It is defined as follows:

struct timespec {
    time_t tv_sec;        /* seconds */
    long   tv_nsec;       /* nanoseconds */
};

An example msleep() function implemented using nanosleep(), continuing the sleep if it is interrupted by a signal:

#include <time.h>
#include <errno.h>    

/* msleep(): Sleep for the requested number of milliseconds. */
int msleep(long msec)
{
    struct timespec ts;
    int res;

    if (msec < 0)
    {
        errno = EINVAL;
        return -1;
    }

    ts.tv_sec = msec / 1000;
    ts.tv_nsec = (msec % 1000) * 1000000;

    do {
        res = nanosleep(&ts, &ts);
    } while (res && errno == EINTR);

    return res;
}