I honestly wouldn't wait for the nursery to comment or advise you on any kind of neurodiverse issues. Not saying it's not a great nursery it could well be, however, they have so many children to keep an eye on at such young ages. Not everything is always picked up on. It certainly wasn't with my children in nursery!
We had to go about getting the paperwork ourselves and getting them on the waiting list or assessments.
Although I'm not saying this is the case.
however if your child happens to be autistic/ It becomes a whole different kind of ball game when it comes to discipline and explaining things to them in ways they can understand depending on the severity.
I have three children, two of them with ADHD. Autism. And both of them are completely different to each other.
Maybe it's time to seriously consider getting him assessed and getting some real support because believe me it can take some time.
I can honestly understand a lot of your frustrations being there myself at times.
But also possibly get his hearing tested. As you just never know, especially as you said he does this yelling out thing. (Could be completely wrong)
Take some time to have a really good close look at certain behaviours, does he get frustrated by touch or the feel of certain things like clothing. Does he like or dislike cuddles/handholds etc.
Is he fussy about foods? Drinks?
And what are his sleeping habits like?
What is he like with eye contact? Not just with you or his dad or anyone?
He may be really struggling inside to try and get across what his needs are to you. But he cannot do that very well, especially at his age. And it's coming across as constant bad behaviour.
Maybe do some more research too on additional needs.
I really hope things work out for the better. Please don't give up hope 💐
Please also keep in mind there will also be a touch of jealousy there for the younger one as they do tend to get a lot more attention. Fingers crossed this will also pass as he gets older too.