In your case (that's a .380, right?) if you carry the same ammo you use on the range, once you prove the gun and are confident/familiar with it, I wouldn't worry further with ammo testing. But that also means you can afford to shoot it more since your carry ammo is not high priced stuff
Back when I carried a .380, I also used FMJ ammo in it, as the JHP's at that time were not considered reliable and many didn't penetrate enough. Over penetration is not the issue you need to be worried about,IMO, it's hitting the target. How many stories have you seen where someone was hit with a pass through? I haven't seen any, outside a war zone. Now how often do you hear about a bystander being hit with a stray round? Happens all the time... moral of the story is that the rounds that miss are of much greater concern than those that hit the intended target.