Could I have a word please?

I'm beginning to feel like I never write a post unless I've got some big advocacy subject to talk about, but lately we've been having some regular kid stuff complicated by disability.  Alexa's growing and learning this year in many wonderful ways, and participating more in her general ed classroom. 
Her understanding of the world and her need to communicate her wants and needs to us have suddenly raced ahead of the vocabulary we have on her talker.  For over a month now she's been having major meltdowns on a daily basis because either A. I don't understand what she wants to do, where she wants to go, what's she wants on her talker or B. I understand but the answer is no (we will not be going to the bounce house every day etc..)  It's like playing pictionary/charades while Alexa is crying and yelling at you...sometimes for an hour or more.
Today she had her first major meltdown at school-I went to find her for library, and she was in speech therapy crying and trying to tell the SLP and the Educational Assistant something that she wanted to be put in her iPad, but none of us understood her signing, and she couldn't spell it.  We eventually got Bob the Builder, a crane, a digger, Thomas the Tank Engine and a couple of other things in there, but she was still crying and trying to say more when we made her go to lunch and I left.  It's really difficult to watch how hard she has to fight for every word she wants to say, but it is good to see her so sure that she can get her point across and to fight so hard for it.  It would be so much worse if she'd given up..
Unfortunately it's pretty hard on me, I don't deal well with her screaming for hours on end, and she always focuses it on me because I'm the one person she knows might understand her.  Unfortunately I can't figure out how to help her accept disappointments.  I've tried everything I can think of, I try to console her for one loss with something else fun, but she holds on so tight to what she wants that sometimes there just isn't anything equally desirable available to divert her from it.   So she screams and screams and signs vehemently and my stomach knots up tighter and tighter.  I can deal with it when she's just mad that she can't have what she wants, that's a learning process that all humans have to go through, but I hate it that I don't know what word she wants sometimes, a kid shouldn't have to fight so hard for words..