I can sympathise with the hypersensitivity thing. A lot of the time, packer/stp or not, any feeling down there can mess with my head. I usually get angry too when noticing it, and a frustration that to me it's not right.
For me, I have no idea how to reduce it, but I recommend distracting yourself from it as much as possible. Knowing that you can feel a part of your body that is wrong is hard to ignore, but the more you dwell on that fact the worse you will feel.
Packing only usually helps with social discomfort for me, and the worry that people will wonder why there's nothing there. When it comes to me, I know it's not a part of me, which sucks. Sometimes not taking off my packer when I get home helps, because it feels like I have /something/ there, other times it's just a reminder of what isn't.
I hope the dysphoria alleviates for you soon, but for now distract with films, music ect. Don't let your mind get to a point of boredom where you can be reminded.