Does this look like birth trauma, OI, or TBBD? Or possibly a combination?

Hi, I'm 33 and had my boy 8 weeks ago. He barely moved the last few months in utero and had an estimated 2 pound growth spurt the week before scheduling an induction. Delivery was very prolonged, lasting 40+ hours with my water broke and ended with a c-section. They tugged hard several times before dislodging his head from my pelvis. He was too big, weighing at 9lbs 10oz. They stated,"He was NEVER coming out naturally." He appeared very swollen especially when comparing him to himself in later photos. On day 2, I gently sat my baby up to burp him and felt what seemed like several vertabre popping. He didn't seem effected by it at all. After pushing on him off and on for 40+hours worth my broke, I figured he was OK and thought nothing more of it. He seemed like a normal newborn Although, one night he projectile vomited about 1 week old. Pediatrician told us to try another supplement. (Late milk production). About 4 days later he became very gassy and it seemed to really hurt him. He would pull legs up, turn bright red, cry, toot, then calm down. After calling his pediatrician, we tried gas drops and took him to the pediatrician the next day. We took his clothes off and weighed him with me, his dad, and the nurse looking at him not seeing anything wrong. His pediatrician came in looked at him and sat down. I asked her about his purple penis and his gas. She came back over to look at him and we saw his elbow was red, swollen and appeared dislocated! We went to ER in an ambulance and this is what they found...

My son at 2 weeks old had 2/20 asymptomatic fractures, all on joints! Only his elbows ever swelled or hurt and only the right elbow ever turned red. The rest were located above both knees, at both ankles, and the rest (showing on x ray two weeks later) were ribs(about 14), connecting to his vertebra. He was vomiting, had constipation, then diarrhea with blood at 4 weeks old, and a temporary cough at 7 weeks old. He also got a mysterious bruise on the sole of his left foot at 6 weeks old and his circumsion became really dark purple upon the original findings at 2 weeks old(I read on several children's hospital circumsion care sites that this could be an infection or his body adjusting.) He had no additional trauma like the suggested mechanisms of injury would indicate. They all sound like he was in a very serious car crash, but he doesn't have any internal damage, no bruising or swelling(except elbows), no shaken baby syndrome, and he didn't seem to be in pain until we saw his red swollen right elbow (except for gasiness).

I know no one hurt our new born son as we were all very excited to have him. His dad and myself happily adjusted our lives in preparation. Please help us. They took our son and I have been searching endlessly for answers. These appear to fit the most: TBBD - several asymptomatic symmetrical factures after low restricted fetal movement. OI - several fractures at such a young age. Or Birth Trauma - Too large for natural delivery discovered after pushing for 40+hours with water broke resulting in pulling several muscles including neck and abdomin. Repeated hard tugging to dislodge his head from my pelvis during emergency c section and first time mom. In some ways, I think it may have been a combination.

Thank you for reading, I eagerly await your response.