If Turkey shot Armenia with a nuclear bomb, given the location and size of Armenia, that'd also affect Azerbaijan, Turkey herself, and, Iran. That means if we shot Armenia with an American nuclear missile, we'd be left in the middle of an interracial nuclear orgy where the US, the Russia (ally of Armenia) and the Iran wipe us out of the world map (quite geographically).
The dirt secret about nuclear war is that Russia and the USA were much more willing to engage in a limited war where each side nuked the hell out of the allies of the other but without directly attacking each other.
There is no way Russia launches a nuclear strike on America on the behalf of Armenia. It would be suicide.