I think I experience a fairly similar reaction with dog barking (it has driven me so insane at times I experienced for the first time in my life what can only be described as “meltdowns”), which for me I have discovered that “action” is my remedy when drowning out doesn‘t work anymore. So I don‘t think you can do that with a kid you need to care for lol unless you get someone to help, but my favourite action is to get up and leave, I get up as soon as I notice it gets too much and go on a walk until I calmed down, usually quite a long one until I find a place without dog barking and can listen to quiet for a bit. Another good action for me is taking a shower (our bathroom is probably the one I can hear the dog the least).