Assuming that the second character of an  a.b element is always a single lower case alpha, here's one solution:

>perl -wMstrict -le
"my  @array = ('x y.g z 123', 'a b.f c 456', 'd b.c w 321');
 my  @include  = qw(b q);
 my ($include) = map qr{ \b [$_] \b }xms, join '', @include;
 my  $second   = qr{ \b [[:lower:]] \b }xms;
 my  $element  = qr{ $include \. $second }xms;
 my @keep =
   grep m{ $element }xms,
   @array
   ;
 print qq{'$_'} for @keep;
"
'a b.f c 456'
'd b.c w 321'
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Updates:

• Changed final  print slightly.
• Changed initialization of  $include scalar.
• Changed definitions of  $include and  $second regexes to insure they can only match single alphas. This could be even more tightly defined by changing the second  \b boundary assertion in  $include to be a positive look-ahead to a  . (dot), and the first  \b boundary assertion in  $second to be a positive look-behind to a  . (dot).