Okay, imma hop in here.
I started PE out when I was 17 and did a LOT of bad stuff. Got injured a lot through the years due to “young man’s excitement”. That, in fact, prevented me from properly PEing, as the injuries I’ve done to myself carried on throughout the years.
Now I don’t wanna scare you, my pain has gone away entirely, for months/years, but comes back when I try to PE, usually a few weeks in when I’m starting to see gains.
I have a VERY similar pain to yours, if not that same one. As you said, there is a fat pad part and a “behind the head” part.
I’ve concluded it comes mainly from squeezes at the base and it’s nerve related. I used to do very aggressive squeezes/holds when I was a dumb youngster and I attribute the injury to it.
However, manual stretching might have something to do with it as well, as I’ve felt the place with specific grips.
Nowadays, sometimes it comes up when I’m jelqing upwards or straight out with a “wide/deep grip” (start gripping from the fat pad instead of base of penis).
My advice is, whenever this pain comes up while PEing, end your session right there, other than that, do everything you would normally (heat/masturbate/sex etc).
Only resume PE when it’s completely gone. When you completely stop feeling the pain, start with a VERY light session and see how it feels afterwards (assuming you don’t get the pain while doing the routine).
I someday hope to be able to write a “complete PE guide to inpatient youngsters prone to injury” but first I have to succeed in getting real gains.