I wear Etymotic Noise-Isolating Earphones in my ears (they are real earplugs with a small hole in the middle through which sound is piped), then I put Bose noise cancelling headphones over my ears, and then I play a rainfall noise through the Nose-Isolating Earphones. This multi-layer approach this works very well for me. The rainfall noise is not distracting to me the way music can be.

I have excellent hearing, and it's impossible for me to solve this problem with a completely passive or noise cancelling approach. Ears will increase their sensitivity until they are able to hear something.

Etymotic Noise-Isolating Earphones: https://www.amazon.com/Etymotic-Research-Noise-Isolating-Ear...

The noise app that I use: https://itunes.apple.com/us/app/mynoise/id813099896?mt=8