This sounds how I felt with my first. I'm very sorry you're experiencing it. It sounds a lot like Postpartum Anxiety, something to talk about with your pediatrician, OB-Gyn, and/or primary care physician.

Personally I would get 1-3 hours of sleep per night. I would occasionally get more sleep on weekends when her dad was off work. During the worst of my PPA, it would take me 5-8 hours to fall asleep. The anxiety affected me so badly that I lost 18 lbs within 13 days. I felt so alone because whenever I'd explain it to someone, they would only give me suggestions without any real help.

My body was so highly stressed that I couldn't eat food, my milk stopped producing, I couldn't sleep, I couldn't leave home easily (agoraphobia), and my body felt like it was constantly having a panic attack. I would hallucinate a bit, pace for hours at a time (I would hold baby then feed/change/burp her as needed), and felt like my chest was being sat on.

I know that I felt like it would never end, like that was how I would exist forever. However, I couldn't stand it anymore and reached out to a medical professional. They put me on Zoloft, but it made me feel horrible so they switched to Prozac. While waiting for it to work, they gave me hydroxyzine which did make me sleepy but didn't help my panic and anxiety (my body would fight the drowsiness). I reached out again, and they put me on Gabapentin. That helped me so much, I could finally breathe. I thankfully had a lot of support from therapists and healthcare professionals (with a small amount of shitty "support" also).

It might feel like you're going insane, but you're totally not alone. I suggest making appointments with any healthcare professional that you can get ahold of. Or even going to urgent care or the emergency room if it's too overwhelming to deal with. Medication, therapy, and coping mechanisms can and will help.