Re: why is 6yr old so annoyed by my babies crying
I think your son may be angry and acting out. The noise of crying may bother him, but that doesn't explain the fighting at school. I think you need to listen to your gut. If you think something is wrong insist on help. Don't take no for an answer. Not from the school or from any Doctor. Talk with the school social worker. That has been helpful to me as my oldest son just started Kindergarten and has had some major seperation issues and has been crying every day. No one would have thought anything of it because once he is in school he is usually fine, but I took it upon myself to involve the social worker. I have had her counseling me on how to help him as well as checking up on him too. It really took me calling her with each of my daily worries to get him on her radar.
I share this with you to say you can bring this up to the social worker daily if necessary. Talk about school behavior vs. home behavior. Talk about your needs. Talk about your DS's needs. (I hope your school actually has a social worker, as maybe some schools don't, ours has two. If you don't have a social worker is there someone in the school who you can talk to like the principal?) Ask for support and referrals.
It is better to have extra help now than to not listen to your gut and wish you had at a later date...