I became a suffer of low frequency sound migraines back when I was working the grave shift. They were redoing the entire apartment complex so when I got home in the mornings All I heard was banging, pounding ,sawing etc. Then the neighbors would have their radio on and the speakers were obviously on the wall between us. I could not sleep. At any little noise especially the bass from radios I would loose my mind. From the lack of sleep I got the migraines. Unlike you were you get them from just hearing the noise.

I wear pink level 33db ear plugs every night still and that was over 10 years ago. I take Xanax every night with 2 maximum sleeping pills and 2 bayer asprins with peanut butter and honey sandwich and Inositol ( a B Vit). I was told it was a nervous disorder by my doctor but if I took the amount of pills he wanted me to I'd be a walking zombie. I learned that lack of B vit make you sensitive to things. Since I have been taking a multi B vitamin the past couple of months I find I have greatly improved with the sensitivity to noises.
I have learned to get around most sounds except the sound of bass and window units. Although every night the sound from the window unit gets less and less.