Looking for a strictly in universe answer, as the out of universe answer is obvious.
A squadron of fighter jets (from any country for that matter) would have seemed to be more affect than most of the avengers that were on screen fighting.
I know shield might normally handle that type of thing, but that doesn't mean the US wouldn't get involved also. General Ross was there so the US seemed to have been briefed on the situation, and they had a CIA operative in Wakanda, so it doesn't seem to be due to lack of knowledge.
Was it something to do with the outcome of civil war?
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.
Wakanda, as you saw when the heroes flew into it, was still being hidden by their illusion field. The US military wasn't even necessarily sufficiently aware of what was going on, not to mention, there was no depiction of anyone asking for the US military to help in that particular battle.
Other than that, up to and including Avengers Infinity War, there was no specific explanation given for this situation.