Some good advice here And I think what you describe in your first para, holding and talking her down, sounds like your instincts are spot on. It's tough, but I'm sure you'll get through this.

Like jackrose suggests, try to get into her head and mirror back her feelings with words. It really does help. She is no doubt frustrated by not being able to tell you what she wants to.
Have you heard of baby sign. It's awesome for helping pre-verbal toddlers to communicate. You could check out your local library and see if they have a picture dictionary you could try. At this age she can learn signs very quickly if you model them for her consistently so she gets the idea. Even just a few signs could really reduce her frustration.

If, for example, she wants lots of mummy time, then try taking some time out for quality mum & bub time. Sometimes the whinging comes when we've been too busy rushing around doing everything else to really spend good time with our kids, know what I mean? I know when DS is like that, if I just sit with him and read a book together for a few minutes, then he's good to go and play by himself for a while again. But if I put him off and try to force him to go on his own again, he just whinges more and more and then the trouble starts...

All the best~~