Perhaps in N. America, we might just speak of a 'noisy argument'.
I believe 'argy-bargy' is derived from the word 'argument'. It's things like this that make me wonder if BrE is more colourful. Possibly someone else from N. America may yet come up with a matching term.
I remember the "argument" between Britain anf Argentina over the Falkland Islands being described as a "bit of an Argy-bargy". An example of the habit of playing with words that is so popular with newspaper headline writers here in UK.
This doesn't help you with regard to an American equivalent, but it may be interesting...
Argy-bargy (also argie-bargie, argle-bargle) noun, UK informal, originated in the 1800s:- 1) loud argument or disagreement which is not usually serious 2) lively discussion, argument, dispute e.g. "There was a lot of shouting in the street late last night. I looked out