system_prompt>my_script.pl $file1
system_prompt>my_script.pl $file2
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If you're really doing this, with no intervening actions, and always having two files to process, you could instead do this:

system_prompt>my_script.pl $file1 $file2
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And then, in my_script.pl:

die "Usage: $0 file1 file2" unless @ARGV == 2;
...
for (@ARGV) {
    process_file($_);
}
...
sub process_file {
    my ($filename) = @_;

    open my $input_fh, '<', $filename or die "Can't open '$filename': 
+$!";
    ...
}
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You have other issues in your code which you'll need to address. One that leapt out at me was this infinite loop:

my $exit = '';
until ($exit) {
    ... code where $exit never becomes TRUE ...
}
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You have two last statements but both are conditional on a pattern match. You should really have a bailout option, i.e. if you've done everything possible in the loop but are still looping, then die, warn and last or similar — and, instead of until ($exit) {...}, use while (1) {...} and get rid of the $exit variable altogether.

sub infile($file1); #will this be passed to ARGV[0]?
...
sub infile(file2);  #will this be sent to ARGV[0] as well after the fi
+rst file?
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Your (commented) questions about passing/sending to ARGV[0] [which should be $ARGV[0]] suggest you haven't really got a handle on the @ARGV array but, unfortunately, I don't know what you haven't understood. Take a look at "perlvar: Variables related to filehandles" and "perlop: I/O Operators". See what both of those sections say about @ARGV: that should either clarify the purpose and usage of @ARGV or, if not, provide you with the basis for more specific questions.