Bharpring asked:
"Are modern bullets made of lead anymore?"
Yes and no. Here is why.
Pure lead is very soft.. so soft you can scrape it with your fingernail. Most civil war bullets for single-shot firearms and six-shooters were made if pure lead. Most modern Civilian-usage bullets are made of what is called "hardened lead" -- which means lead alloyed with another metal (such as tin or antimony) to make the lead less soft. (See the 1886 Winchester bullet lead-alloy "recipe" attached at the end of this post.) The softness created a problem when using pure-lead bullets in rifled firearms. The sharp edges of the gunbarrel's rifled grooves tended to shave a small amount of lead off the bullet as it traveled down the gunbarrel upon firing. Eventually that caused a buildup of lead shavings in/on the rifling-grooves, enough to interfere with repeater firing and accuracy. The gun makers and ammunition manufacturers adapted to that problem by switching from pure-lead bullets to "harder" lead-alloy bullets. (And eventually, switching to metal-jacketed lead bullets such as the Colt ACP copper-jacketed bullet.)
In the information above, I said most Civilian-usage bullets are a hard-lead alloy. I should mention, since the development of automatic firearms, most Military-usage bullets are copper-jacketed. But of course, Civilians can purchase and use that ammo. See the photo of a sawed-in-half copper jacketed and a metal-jacketed bullet, below.
Bharpring, I'd lioke to help you identify your bullet, but to do so I need to see well-focused CLOSEUP photos of it, made after you scrub all the dirt out of the bullet's body-grooves. Right now it kinda-sorta looks like a damaged civil war .44 Colt, but there are several other possible identifications. Also, if there are multiple tiny parallel raised ridges inside the bullet's body-grooves (see another photo below), it is from sometime after the end of the civil war.