This is the age and they do this.
They will scream/yell because this is the only way they can communicate.
It's normal.
It's not easy for the Parent, but other stages will come up.
Teach her sign language for functional words. ie: "help", "eat", "more", "drink", "stop", "up", "no", "come" etc.
Also, they get "separation anxiety" at different age stages. So this is an element in it too. As toddlers, when older, they will go through this too.
For a child this age too, they don't know the difference between "now" and "later." Everything for them is about the "now" and immediacy. So well, it's not always easy.
But one thing, frustration can build up for BOTH child and Parent, when they are expected to "act" older that they really are ready for. Everything, and expectations, needs to be age appropriate.
In everyday life, and needs... we can't pick up our child at every cry or scream. Sometimes we just have to wait a bit, because maybe we are using the bathroom, or in the middle of cooking and our hands are dirty with raw food stuffs, or we are in the middle of a phone call. Well, so as long as our child is not in "danger"... it's okay. Let her know with your voice, that you ARE right there.... and with facial expressions try and "show" her.
Wordy explanations don't work well at this age. They won't follow along. Also, at this age, they do NOT have "impulse control." So even if you tell them "no", they will do it again. FULL IMPULSE CONTROL is "developed" and it will not develop until about 3+ years old... so you'll need to keep this in mind, and keep expectations toward the child with this in mind.
Kids get used to repetition and routine. So, whether positive or negative... this is what they will respond to or get used to. And their reactions will be in reaction to it.
Kids this age are "reacting." They don't do things yet "at will." It is ALL per their development and age set. ALSO, they are still learning about cause and effect. Even at older ages they are still learning this. It's okay.
I would not do time-outs at this age... but some do. It's up to you.
It will not necessarily get "better" once she talks... because as is normal, each age development brings another set of developmental age "issues." And, as a head's up, not only is 2 years old a hard age, but at 3 years old... this is harder in another sense. ALL the while, their personalities and cognition is changing. And their sense of "self" and independence.
Even their "emotions" are STILL developing....and they don't yet know how to understand it or abstractions like this. So, this frustrates them too.
Perhaps, get some books on age development. Each age, has it's own unique set of issues and frustrations and pleasures. :)
A child spends their life learning about "our" rules and needs...but what about them? In order to create our child and raise them and "teach" them and understand them too... it's important to FIRST understand the child, at each age. A good book is "Your 1 Year Old" (you can get it at amazon.com). It's a series for each age.
It's hard, but don't pressure yourself. We will be "teaching" our kids their WHOLE life. That's a long way to go! LOL.
And a lot of times, we Moms are trying things on the fly, spontaneously. It's okay. We have to learn about them too.
Your girl has only been in this world for 16 months...and is only beginning to learn our rules. Her behavior is normal.... but teach her and decide HOW you want to teach her. Consistency is important for kids. "Discipline" is about teaching... not about "right/wrong" or about punishment necessarily... and about boundaries.
Yes, it's a phase. Yes, lots more will come up. EEK!
It'll be okay. Just see what works for you... and her, as long as it is not harmful.
take care,
Susan