Right now the only way your DD can communicate is with crying. It's so hard to think of crying as communication -- it's unpleasant to the ears, and we're conditioned over years to regard other children's crying as annoying or as them acting 'spoiled'.
But at this young age, they have little control over their bodies except for their voice! She can't really use her hands very well, she can kick her legs, but it's random kicking not controlled. So the only way she can really react much is to use crying.
Distraction is the best way to deal with babies, really until 18 months old distraction will be your main tool! I think using a stern voice doesn't work very well anyway, for the most part. Children respond better to honey than to vinegar, if you know what I'm saying!
You'll find that if you sing to her, use fun rhymes, or make funny faces that will quickly get her to stop whining or crying while doing those unpleasant things. And really, who can blame her? It's no fun to have someone putting cold wet things on your bum or to wipe at your nose which is a very sensitive spot. heck, I whine to myself when I blow my *own* nose -- it often hurts!
You'll get so good at distraction over the next year. You'll learn the things that absorb your DD and things that don't really phase her or interest her. For diaper changes, what's always worked best for my son is singing a song where I insert his name in the lyrics. So, "Old MacDonald" becomes "Owen Finn had a farm". That makes him giggle. She won't recognize much, but she will learn her name over time and that will really please her. Another good thing to do during diaper changes is to tickle/kiss/nuzzle toes. That is very pleasurable. I usually start a diaper change with that stuff, then once he's giggling and happy we quickly change the diap while singing, then end with a cuddle.