4-month-old discovering will and voice

Hi! Our 4-month-old used to be a super easy-going baby, but more recently she has become more difficult. When we put her down somewhere, she wants to be held, but if we pick her up she won't necessarily be happy with that, either. She has definitely discovered her voice and will yell and whine in protest if we do something she doesn't want. It's not crying, but can turn into loud screaming and crying if we don't respond right away. Now my question is this: I remember everyone saying how you can't spoil a newborn, and I remember asking my pediatrician when that rule no longer applies, and she said at 3 months. So now I am not sure how to respond. If I pick my daughter up every time she indicates that she wants to be held, am I teaching her that if she only yells and whines enough, she will get her will? I certainly don't want to reinforce that behavior. On the other hand, I don't want  to traumatize her, either. She is only 4 months after all. I am curious if anyone has any advice on this? Do I pick her up right away? Wait a while? Do something entirely different? Thanks!