The short answer is "No". .38 special is a revolver round and .38 auto a.k.a .38 ACP is for as the name implies "Automatic" pistol. The cartridge of the .38 auto is not even rimmed and would fall straight through the cylinders of a revolver, if it even fits. The bullets and cartridges also have different dimensions, and thus different firing pressures.
More info: Wikipedia
.38 Auto (ACP)
.38 ACP - Wikipedia, the free encyclopedia
.38 Special - Wikipedia, the free encyclopedia
And congrats on your new hardware.