Congenital? No. Acquired? Yes. The area of the brain that processes and interprets sound has to develop. Without sound input as a child, that won't happen.

Current leading theory of tinnitus is called the 'central gain' theory. This is where the brain becomes accustomed to seeing signals from the ear at a certain level, and when that neural level is no longer at that level it will add in its own noise to make up the difference. This noise is then perceived as a tone or sometimes a broadband sound, commonly described as either a ringing or a whooshing sound. Sometimes it can also be described as crickets. Depends on the person and cause. Not all hearing loss comes with tinnitus, but most tinnitus comes with hearing loss. In audiology school we had a whole class on tinnitus and covered many interesting aspects exactly like your shower thought here and went over papers on every angle you could think of. It was fun. But in the end, the brain has to at a minimum know what sound is to even perceive sound.