Which is correct PM or p.m.?

There are many ways to write the abbreviation for "post meridiem." It can be in capital letters, small capitals, or lowercase, with or without the periods. How it's written is a matter of style. In print, it is styled a certain way according to the decision of the publisher.

Most commonly it is seen with the periods, and in print it is usually written in small capitals. So "p.m." is more customary and familiar than "pm." Whichever you do, though, do it consistently within a given document or piece of writing. If you are writing for publication, style it the way the publisher does, or expect to see it changed by an editor.