Update:

Solution which still uses core module Time::Local:

use strict;
use warnings;

use Time::Local qw( timegm_nocheck );

# birth_date_age(2006, 4, 28) for people born on April 28th, 2006.
sub birth_date_age {
   my ($bday_y, $bday_m, $bday_d) = @_;
   
   # ----------------------------------------
   # -- Get current date.

   my ($now_y, $now_m, $now_d) = (localtime)[5,4,3];
   $now_y += 1900;
   $now_m++;
   my $date_now = timegm_nocheck(0,0,0, $now_d, $now_m-1, $now_y);

   # ----------------------------------------
   # -- Get next birthday.

   my $date_next = timegm_nocheck(0,0,0, $bday_d, $bday_m-1, $now_y);

   $date_next = timegm_nocheck(0,0,0, $bday_d, $bday_m-1, $now_y+1)
      if $date_next <= $date_now;

   my ($next_y) = (gmtime($date_next))[5];
   $next_y += 1900;

   # ----------------------------------------
   # -- Get prev birthday.

   my $prev_y = $next_y - 1;
   my $date_prev = timegm_nocheck(0,0,0, $bday_d, $bday_m-1, $prev_y);

   # ----------------------------------------
   # -- Calculate age and others

   my $age = $next_y - $bday_y - 1;

   my $days_to   = ($date_next - $date_now) / (24*60*60);
   my $days_from = ($date_now - $date_prev) / (24*60*60);

   return ($age, $days_from, $days_to);
}
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Notes:

• On years without a Feb 29th, March 1st will be considered the birthday anniversary of people born on Feb 29th.

• I leave the date parsing to the caller. It makes for a more flexible solution.

• For arguments, days, months and years are one-based.

• Internally, days, months and years are one-based.