I've never heard or read about GD in your privates. Where was your biopsy taken from- torso, legs, privates?
You could be like me and others and have multiple forms of eczema. My Allergic Contact Dermatiis affected various parts of my body, not just outside with itchy rashes and red welts but inside with random crawling, lazer like stinging every 15 seconds, worse at night. I was going crazy from lack of sleep, ready to end it all. My 5 Day Extended Patch Test identified my allergens and I am dilignet, a real challenge because I have so many, but I conrol my diet, enviroment and contacts and am free of symtoms.
My GD papuales never got infected. Is the white gel pus? You could have pustuales, infected papuales. Witch Hazel is mildly antibacterial, try splashing with at the end of your shower. I had classic GD, front and back torso from the neck to about my pubic hair or butt crack. My intial outbreak lasted one year. As I have mentioned, my cilantro smoothies and diet change have kept me clear since mid 2019, and I do drink just plain cilantro now at least 2-3 days about every 2-3 weeks. I don't like the taste, not much can be done to improve it so I just blend it with water and chug it down without breathing. Hardly notice the taste that way.
So very sorry for your suffering. I understand and you must keep searching. This chelates the blood, removing heavy metals, and helps about 40% of those I blog with.
See multiple dermatologists and keep blogging on this site and others. I've learned so much from others.

Wash with a lard and lye soap like Grandma's. The lye is converted to glycerin so all you contact is lard and glycerin.
Have you had testing for other forms?
I didn't get bumps, just redness and swelling and I didn't get a crawling feeling. In my private part I did have intense burning and itching. What helped after years of dealing with that was giving up processed sugar and the Estring is a silicone ring of time released estrogen. I am allergic the inactive ingredients in all vaginally inserted estrogen foams or creams and at my age doctors don't want to prescribe estrogen tablets. This silicone ring has restored my vaginal health, rebuilt my tissues. So diet and localized estrogen have been a miracle for me.