HELP - 6 Days PP - breastfeeding issues

My son is 6 days old and I was planning on exclusively breastfeeding. I have a fair amount of scar tissue on my nipples from old piercings (they stayed infected when I had them & made my nipples generally more sensitive/painful)

Right after he was born, the latch hurt. And yes, it was a proper latch, the lactation consultant in the room even confirmed. They were impressed by how well we did, but it just hurt so much. I pushed past the pain, but I genuinely felt he was not getting anything. We tried expressing colostrum at the hospital and only got a drop. We tried a nipple shield, but that didnt seem to work.

A fee days ago the pediatrician said if we wanted to we could supplement with formula. I didnt want to but between his major weight loss, dehydration (the pediatrician was most concerned about the dehydration-he only had 2 wet diapers in 36 hours) and his slight jaundice, I felt like it wasnt fair to deny him some sort of nutrition. So what I started doing was this:breast feed on demand as I have been doing, and syringe feed at most 30ml of formula every other feed. This got him up to 8 wet diapers a day and his weight back up, also his jaundice is starting to clear up. The pediatrician said we could lose the formula but I am so scared he isnt getting anything from my breasts. I mean, I feel like he is only getting drops and I cant have him latched 24/7.

He is perpetually sleepy at the breast. I massage myself, touch his cheeks and chin, try to relax, etc - I dont see many signs of him swallowing. Sometimes it seems like it is just for comfort so I just hold him but he starts rooting and getting fussy so I put him back on. He is never, never satisfied after a feed. I feed him so many times per day, it is WAY MORE than 12 times per day.

One breast feels painful and there are giant lumps in there. I try gently massaging, cupping, and touching them during the feed. It feels like there is milk in both breasts, but I can only hand express drops.

I am waiting on a pump so that I can store any extra milk, or maybe switch over to pumping if that will work better for him.

I really need advice. And please dont tell me "oh just feed him on demand" or "you must have an improper latch" because I am doing those things.

Do I have a letdown issue? What is going on here? It is really affecting my mental health and making me feel like a failure. I never, ever wanted to touch formula I was so against the idea. I want to provide for my baby but it feels like I cant