Noise-cancelling headphones

I've been wanting noise-cancelling headphones for a while, because I really cannot stand the sound of children and sometimes I'm stuck in public areas where I really cannot avoid them. But are there any headphones that block out those high-pitched shrieks? I know noise-cancelling headphones used to be crap at irregular noises, but I don't know if that has improved. And they're not cheap, so I don't want to just take a chance.

I don't mind low-pitched repetitive sounds like plane engines which is what most of them seem to focus on blocking. It's those shrill sounds that give me a headache and make me feel murderous. Right now I use earplugs, but even then, I can still hear the little fuckers shrieking and wailing.

Suggestions, short of becoming a hermit or inducing deafness?

Hearing protection devices are effective at continuous background sound (machinery, droning airplanes, normal conversation etc) but are way less effective at mitigating sudden, impulsive sound (gunfire, screams) particularly high-frequency. I suppose if you're talking music headphones rather than strictly "shooting headphones", then maybe music might cover up some of the noise.. I've thought about getting a pair for airplane flights, but at this time I just can't justify the $$$.

Overall, noise-cancelling headphones are certainly better than nothing!

Actually, I am thinking that maybe what I want are custom earplugs. Being able to hear music is less important to me than not being able to hear assholes. My current solution is earplugs, or in-ear earplug-style earbuds. I borrowed someone's shooting ear protection once and gave it a try, but it didn't seem to help against infants. Anyhow, I understand that if earplugs are made to fit your ears, they are way more effective than the cheap ones.

I'm willing to spend $$$ if it would actually work, because screaming children not only make me angry, they are a migraine trigger. It's just I've never seen this particular issue being addressed in reviews, and I don't want to pay $300 for something that can't perform what I see as the primary function.

I started wearing ear plugs years ago because the apartment I lived in was really noisy from banging pipes in the bedroom. Now I have to sleep with them or I can hear every. frickin... little noise that happens and it wakes me up. Also, the ear plugs can hurt sometimes when I leave them in for too long. I've been trying to wean myself off of them, but I think I've become hooked on them.

I also want to mention that prolonged ear plug use can affect hearing, cause wax impaction in the ears and ear infections. I think short term use is fine.