There are a few reasons I can see why the US military didn't/couldn't help during Wakanda battles.
At the end of the Civil War, everyone was a wanted criminal or had disobeyed the US Government. So, why would US military assist them? In Infinity War, the following conversation goes on between Cap and the secretary.
Secretary: The world's on fire. And you think, all is forgiven?
Captain America: I am not looking for forgiveness. And I am way past asking for permission. Earth just lost her best defender. So, we're here to fight. And if you wanna stand in our way, we'll fight you too.
Rhodes was the only person left who could ask for assistance, but he also throws it away by declining order from Secretary about arresting Captain and others.
Rhodes: That's a court-martial.
If you remember, they went to Wakanda to remove the Mind Stone from Vision. They knew that Thanos is coming to get the stone, but no one knew that he will send the Black Order with an army to retrieve it.
The war started all of a sudden in a nation where US military is not present at all. There was no time to call for the military assistance. And during the battle, Thor showed up. After which, they hardly needed any military assistance.