Nested bean sack work?

Iy

Long post

It's a bit confusing but I'll try to tell you what's happened. Since about 2 and half months old my son has started eating his hands a lot. At the end of Sept he was sleeping through the night for about two weeks and then he started his 3 month growth spurt. So I nursed him every 2 hours day and night for 10 days solid! After that ended his teething pains kicked in and he woke up 7 to 10 times a night in pain or gassy from eating his hands. I bought him an amber teething necklace and literally that night he wore it he went to waking up 3 to 5 times. So he's been like this since the end of Sept. I dont know about his teeth. I think they broke the surface and went back down because starting on a Thursday he just cried all day and night. It was a few days later on a Sunday that he stopped being fussy during the day and at night though he still wakes up to eat every 3 hours. So I think the pressure is off his gums by them breaking thought but going back down because the skin looks and feels like it separated and we could see the teeth at the surface during his super fussy time. Thank you if you've made it this far reading lol

So do you think this nested bean aack might help him sleep longer? His teething pains are at a low right now.