Thank you for all your input everyone. I dug it in a place where the soil only goes a few inches deep before it hits a huge slab of limestone, so I was hoping it might be quite old even though it was shallow.
Looks to be a common lead RN pistol bullet. Still manufactured for many calibers. Since .38 is among the most common, and the size looks correct, that would be my guess. Definitely not FMJ, but the caliber is hard to determine without measuring with calipers etc.