I was in a similar position not long ago myself. Little one would not nap in the day in the cot without a long period of crying which was distressing for us both. I would rock, cuddle, feed, walk in the pram or go for a drive in an attempt to comfort him. He would be so tired but just unable to settle. Bedtime would be a similar story, rock or walking with a very unhappy baby until he fell asleep then cautiously transfer him to his cot and hope he would not wake. Often he would and we would start the process again.
Once he was successfully put to bed he would wake every hour throughout the night. Inconsolable. Sometimes breast would comfort him for a moment but he didn't seem to be taking much at all. I was on my knees. My partner would help, but weeks of being woken every hour for anything from 10 minutes to a couple of hours takes a huge toll on your mental health. I had never felt so down and really struggled in my day to day life.
We saw a gp who diagnosed reflux and so started with gaviscon. We also implemented a bedtime routine, bath, story while being fed and then bed.
The gaviscon made a slight difference I think but baby was still unhappy at bedtime.
As an absolute last resort we attempted controlled crying. I felt awful about this decision but little one was so distressed before bed while being held I thought worst case we try for a day or two and then stop. We discussed what we felt comfortable with and set time limits, I didn't want to leave it longer than five minutes to pop in and we agreed to stop if after 45 mins baby didn't settle.
We had a few days of getting baby used to our routine, and then maybe four days in we put baby to bed after the last feed, awake. Said goodnight. Gave a kiss and left the room. He wasn't happy. My partner returned after two minutes and said goodnight gave a kiss, hand on chest for a moment and then left. I went in after another three minutes and then left. By the time I walked to my room to sit with my husband to watch the monitor and count down to the next visit, baby fell asleep. I spent most of the night staring intently at the monitor waiting for baby to wake any moment. Next thing I know it was 6am and baby was awake. We steeled ourself for the second night beging worse as everything I have read has suggested this.
We followed the same routine, baby in cot awake. Partner popped in after two minutes of grizzling. Baby fell asleep. Again right through until 6am.
Third night we did not need to pop back in at all. Now we continue the same routine. Baby popped in cot awake and asleep often by the time we walk downstairs. Every parent is different and I appreciate this is not for everyone. I was very conflicted about trying this.
I guess somehow we were stopping baby from settling himself to sleep. I'm not suggesting you try this, just sharing my experience. I can fully understand how it feels living with the lack of sleep!