I can't offer any more help in the "medical explanation" department than others here already have.
But I wanted to tell you how badly I could relate.
My parents' disregard for my noise sensitivity is what ultimately forced me to live in a van on the streets alone, even when I was too ill to care for myself. I'd spend days unable to drive or walk, and nearly died a few times from lack of a caregiver. Strangers saved my life more than once. This way of life was far, far better than having a caregiver with my parents but having all the noise exposure.
I have since realized that being around people who will not respect your wishes is super harmful. Period. You shouldn't need a good explanation, you shouldn't need to prove it. Getting out in the world was such an eye-opener....people who care about you don't demand proof! They either (attempt to) accommodate your stated needs, or they say they can't and they're really sorry.
The ability to control my own environment was key to recovering from the hyperacusis. Living in a vehicle, I could usually get away from any noise that was problematic. When staying with my parents, I couldn't escape the noise and the resulting trauma contributed to my PTSD diagnoses. PTSD and sound sensitivity are, or can be, very closely linked.
To this day, when I visit if they do any sort of controlling or blatantly inconsiderate behavior around me, two things happen. First, I mentally brush it off. Then, I discover I'm absolutely disabled by noises that were completely fine even 10 minutes ago. I mean total collapse, hands over ears, unable to move, horribly traumatized, crying in pain. But not from whatever my parents said or did this time, it's just the reaction to the noise. It tends to continue for about a day or two after, even when I've left the premises and and am not in that environment at all.
Please don't underestimate how badly this could be affecting your health and healing. For me, my recovery absolutely required an environment where I could consent to which noises I was exposed to and for how long. This is also why living with roommates/housemates is out of the question for me. Noise exposure is like someone touching me - if I've consented to it, it means I'm up for it and it'll probably be okay. But if I'm lying there trying to rest and noise exposure happens nearby, it's like someone is touching me without my consent. It feels as traumatic as assault, because of the physical pain involved and the fact that it's being done to me nonconsensually and I can't make it stop.
I don't believe for a second that hyperacusis is psychosomatic. But I do believe that repeated trauma you can't get away from is like POISON to the nervous system. It will worsen pretty much everything and interfere with potential healing that could otherwise happen.
Take care and I'm wishing you all the best.