M.F.
I'm sorry you're having problems. I don't believe a child that young can be "spoiled". She is too young to understand how to manipulate people. If she is crying to be picked up, its because she needs and loves her mommy. Maybe you can try wearing her in a sling or wrap, then she can get the closeness she wants and you can get something done too. I recommend Jonesling, Belle Maman and Trendy Tots carry them and they are wonderful. When my son is fussy and nothing will work, a few walks through the house in his sling and he's out.
As for the nap, my son was the same. So what I did was take naps with him for a few weeks. Then start sneaking away after they fall asleep and stay close by and respond quickly when they start to stir. Then I think they trust you will be there and they can relax and sleep longer. I personally don't listen to people saying you will spoil a baby. A baby's needs and wants are the same thing. I hope some of this helps......M.