Just use a magnet on the cylinder to see if it's steel or alloy. As I said, it's highly unlikely that you have an alloy cylinder .38 M&P Airweight (pre Model 12), but it only takes a second to check and be sure. (As DPris said, model numbering wasn't started until a few years after your gun was shipped, so you won't find a model number on it.)
I'll add that while it may be safe to shoot +p in the gun, it doesn't necessarily mean it's a good idea. Unless you plan to use the gun for SD it's really not necessary (and maybe not even then). If you do plan to use it for that it would make more sense to do the bulk of your practice with standard pressure loads, fire a few +p loads so you know what to expect - which shouldn't be all that different - and then load the +p when you carry.