Help...my son is a squealer

And not the squealing in delight kind.  He is the high pitched, ear piercing, windows breaking, steam blowing, I'm not getting what I want kind of squealer.

I am mortified.

I don't know how this happened.  I don't squeal, his older brother didn't squeal, he is not around other squealing children - why does he do it?  BC (before children), I used to silently tut tut parents of children who were squealers "How can they let them get away with making that sound", "What a spoilt brat?" - I am ashamed I was so judgmental.  

I honestly can't seem to stop him from doing it.  He does it when he can't have his own way.  Being 16 months old, there are alot of times in the day that he can't have his own way.  He can't stick his fingers in the powerpoints, he can't pull his brothers hair, he can't press every single button in every elevator we get into, he doesn't want to get in his stroller etc.  Each time I tell him "No" he lets out a toe curling squeal.

I get so embarassed when I am out and about.  It is so loud that everyone can't help but look.  They must think I am torturing him.  All I can do is shush him or feed him...but I don't want to shove food in his face every time he does it - its not really a long term solution.  I don't want to not go out.  But after a particularly bad incident on the train the other day, I feel like I am at my wits end.

I have tried giving him the words to use, distracting him, putting him in a time out, ignoring him, getting cross, even putting my hand over his mouth - nothing seems to work.  I never give him his own way just to keep him quiet as this seems counterproductive so I am trying to work out a way of dealing with it that will help me in the long term.

I keep telling myself that it is just a phase - he will grow out of it once he has more language and can communicate better - I hope this is the case.  I think I am going to just keep ignoring it - its all I can do.

Have you had a child who is a squealer? What worked for you?