The one in the Mexican War (1847) was the subject of a popular Currier and Ives print (can be seen at American Memory). Four dead or wounded soldiers are in the foreground.
Sheet music by Charles Grobe, 1847, at American Memory. No real lyrics, but a running commentary on what the music is representing.
A similar piece, by Wm. Striby, 1850.

More likely is one of the broadsides. One, dedicted to the Buena Vista Guards (Civil War) was sung to the tune, "The Girl I Left Behind Me." Also at American Memory. Enter -Buena Vista, song- in Search.

But this is the one you are looking for: "The Dying Soldier of Buena Vista," by Orramel Whittlesey, 1849:

On Buena Vista's bloody field,
A soldier dying lay,
His thoughts were on his mountain home
Some thousand miles away,
His thoughts were on his mountain home
Some thousand miles away,
He called his comrades to his side,
For much he had to say
In briefest time to those who were
Some thousand miles away,
In briefest time to those who were
Some thousand miles away.

I know 'twill grieve his inmost soul
To think that nevermore
I'll sit with him beneath the oak
That shades his cottage door
I'll sit with him beneath the oak
That shades our cottage door.
But tell the time worn patriot
That mindful of his fame
Upon this bloody battlefield
I sullied not his name.
Upon this bloody battlefield
I sullied not his name.

Enter the title in Search to find the sheet music: Search