No this is actually right. Accept that your day has started at 3am and there's no more sleep for either of you, etc. half the trouble with young children is the anxiety, checking they are still breathing, mistaking a cats yowl for your crying baby. Acceptance and trying to relax into it is really important.
My second child was a much harder baby objectively, but because I was more chilled out second time around it was easier for both of us.
We had to pace for 30minutes every night with DD. She had to be asleep and then wait another few minutes for her to get to the floppy stage before we could get her down. Like you op, it knackered our backs and we both needed physio. Eventually we cracked an sleep trained when she was a year old. First night was bad but then improved massively on night two, been great since with barely a blip. They are 4 and 6 now and sanity has slowly been restored for the last two years.