Was reflux ruled out?
I feel I could have written your op - my DS is 16 weeks and very similar.
We are starting to come out the other side though.
Firstly, we got reflux medication at 10 weeks
Secondly, he surprised us one day. I had a stomach bug and needed the bathroom without him. Put him in sleepyhead and thought I'd have to deal with the crying. He fell asleep after a few mins! I too hated the thought of crying but now I just accept he cries for a few minutes with me patting and shushing.
Thirdly, I got tough with a routine at 14 weeks
I start each day as brand new at 7am.
Feed till I know he's full, both sides if necessary.
Play for an hour.
Nap. This is car, pram or sling. I tried to stay out until the hr was up. It was then 2and a half hours since last feed so I'd repeat the whole pattern.
I'd go be bed about 8pm with him, in my arms but with him lying down (only possible since getting medication). When he wakes, I try burping, walking, shushing. Feeding is a last resort as every 45 mins was a killer. I also use ewan.
Getting the day naps in helps, and made the nights easier (as in an hour and a half instead of 45 minutes) plus it gave me structure.
Things aren't amazing yet, but they are better. Each week is slightly better. I've had a couple of 3 hourly stints and he will go down in his sleepyhead (warmed with a hot water bottle) at night after feeding. Not always, but I do try each time.
Oh and a dummy helped too. He hated that but I kept with it and now it's a sleep cue.
Its so hard, I know. X