Technically, I don't think "foaming at the mouth" has anything to do with anger or annoyance. I thought it had to do with craziness (referring back to rabid dogs foaming at the mouth). But I suppose maybe people do use it in connection with anger?
never heard expression 'fit to be tied' or the word 'conniption', despite having some friends in New England. Don't think we use either of these in UK or Ireland.
I remember it from my youth in 1980s Nashville, though I remember hissy fit being used more. I hadn't thought of/heard it in years, but conniption came right to mind. Time for some Country Time Lemonade on the veranda. I still love Nashville, FWIW.