Hi T.,
Hmmm... so I know this is going to sound like the advice you DON'T want, but what I encourage you to do is to hold her more, and give her the attention she wants. Let me plead my case... =)
At 22 months old, your child DOESN'T know how to be manipulative, and you aren't spoiling her by picking her up. You are her "go to" person, and although this is incredibly draining for you, that's how she sees it. You are her "it" person - the one she knows is going to be there for her no matter what.
I encourage you to hold her more, snuggle her, cuddle her, and if she's fussy, talk to her and say things like, "What are you so fussy for, baby? What do you want from mommy? You want mommy to love you more?" And of course, you could give her some gentle "shhhshing."
I realize you're trying to NOT pick her up so much, but the reality is, she is communicating a need to have you close to her. At this age, she really needs and wants it... kids don't start to develop their independence and wanting to be away from you until well into their 3rd year. So trust me, there is PLENTY of time for her to develop independence and you absolutely are doing NO HARM by coddling your baby at this phase.
There is much research to support this: I encourage doing a little research at ZerotoThree.com for more information. I am happy to provide research as well (I'm a "research" person, so please forgive me... it's just that we hear so much advice all the time and I personally like to know where all the advice comes from!)
Take care, good luck. =)