Somewhere I read the Chicago Manual of Style allowed for the periods to be removed, but now I can't find it. Thanks.
Indeed, a matter of style rather than absolute correctness. The Chicago Manual of Style (14th Ed.) says to use capitals with periods, while it seems far more common in British English to use the lowercase with periods (as per The Economist, Times, and Guardian style guides). However, The CMS also says that usage without periods is acceptable, but, lest we forget, AM could then be confused with the radio frequency. What is most important however, whichever you plump for, is to strive for consistency, and, it would appear, should you be lucky enough to be accepted by a published, chances are they would have their own style prescription to adhere to anyway.
Associated Press style is lowercase, with periods, don't do the :00 part if it's an exact hour. I.e. 2:30 a.m. 2 a.m. Don't say "yesterday morning at 7 a.m." because that's redundant, saying it's morning twice. Hope I helped at all!
I don't know about recent changes, but the head of my college professional writing course insisted on the periods. :/ Don't know if that answers anything, but if Gannon says the Chicago Manual of Style says they're optional, I guess they're optional. dnsralg's suggestion seems safest, though. I'd go with that and continue to look around. I don't have my CMS around right now, but I'll check it out later. I suspect I'll get the answer that Gannon mentioned, though.