A: The problem here is that there is a disconnect between a 16 month old's idea of what "No" means and a 16 month old's idea of its implications. A baby of 16 months thinks in very black-and-white terms. When you say, "No!" because you want your daughter to learn not to put your cell phone in her mouth, she understands that you want her to stop. But she also concludes that she is a terrible person who deserves to be beaten up for it. She goes ahead and beats herself up, just to show that she's really learned her lesson. This is how babies that age think.
My suggestion is that you postpone saying "No!" to her until she shows that she can tell the difference between simply stopping something that you don't want her to do, and taking over the job of punishing herself physically. A 16 month old is still little enough that you can get her to stop mouthing your cell phone just by taking the cell phone away from her. You don't need to try to teach her anything. All you need to do is prevent her from doing dangerous things.
You can start explaining, "No no, we don't pull the cat's tail" when your daughter is old enough to have a conversation about cats and the fact that they have feelings too. Right now, just keep your daughter safe and leave the "No!" until later.