Sensory processing disorder associated with autism is exactly what came to my mind because it's exactly what I deal with. I usually shut down instead of melting down, but kids playing at anything past a barely-audible level is extremely difficult for me. Other attention-grabbing noises are also difficult, like dogs barking, car doors closing, people yelling, etc., and other stimuli cause me to shut down too, like dogs jumping/breathing on me (basically everything about dogs, unfortunately) or someone touching the back of my head/neck.

It took a lot of research into how my sensory processing reacts to different things, and I still struggle frequently, but I'm a father now and most days I'm very happy about it. I have noise canceling headphones for when I get overwhelmed, and I keep a clicky mechanical keyboard switch and barrette in my pocket to fiddle with, which helps a lot.

OP, I can obviously only speak from my own experiences, but I think dissecting what exactly causes these sudden emotional bursts and finding sensory distraction or blocking techniques to dampen them might work for you too. Headphones are a godsend.