It sounds like testicular pain like that could be due to contraction of the cremaster muscle, which essentially controls testicle height. Its main role is to help regulate temperature in the scrotum by controlling how close the testicles are to the body. This is important because a very precise temperature is needed to make sperm (just a little colder than core body temperature).
I couldn't find anything to suggest that high-pitched sounds cause the cremaster to contract. However, there is some evidence to suggest that activation of the sympathetic nervous system (the "fight or flight" response) can cause the cremaster to contract.
In this study the authors state that there is a
reduction of myogenic responsiveness secondary to the elimination of
In other words once the "fight or flight" response was disabled in these rats, the cremaster had less of a response. This indicates that the cremaster responds at least in part to the sympathetic nervous system.
My suspicion is that testicular pain in a situation like you described is due to contraction of the cremaster muscle. This was most likely caused by a sympathetic "fight or flight" response caused by the screaming/ confrontation. I don't know of any mechanism directly linking high-pitched sounds to the testicles.