Oh good, when you said sibling I was worried you were in your teens. Don't let her hide her head like that when sitting on you-- avoid shadowy spaces (I know it seems innocent, but it's not a good habit to encourage due to future hormones)...Mine tries to do this if she is allowed to sit on my lap.. No shadowy spaces.
By petting her to "calm her down" you are rewarding the behavior. You MUST teach her independence because there is so much wrong about this current plan. If a toddler screams and cries for a treat and you give the toddler the treat to make him/her get quiet, that's a problem, and a similar situation is going on here, only your attention is the reward. She thinks- "when I scream, you come back and pet me ...so now I scream to get you to come and pet me. I want to be with you 24/7, and I am a flock animal so I want to be with you all the time, but if you ever leave, I will just scream and you will come back."
Cockatoos will become as needy and obsessive as you allow them to be....It is not healthy to over-indulge their velcro-tendencies. Their threshold for interaction/attention is insatiable (to the point of self-destruction)...Which is why you have to help your bird and stop giving in.
When you leave the room, see about how long it takes for the screaming to start. DO NOT return until she is silent for a set period of time, based upon how bad the problem is...If it generally starts the second you are gone, then I'd start low at 5 seconds and gradually work my way up to 10, then 15. This is a "I Mississippi, 2 Mississippi" count..If she screams before 5 seconds is over, the count starts back at one until you get to solid 5 s of silence. At that point, enter the room immediately and say "thanks of getting quiet" in a quiet voice and praise. You may have to deal with her screaming for a few hours...Once the screaming starts cut off all forms of attention. DO NOT enter the room for any reason. DO NOT look at your bird or talk to your bird if she is screaming. You have to wait a full 5 s of silence before any form of attention (proximity, eye contact, talking etc) are resumed-- Make sure you tell the whole house this set of rules because one person can mess it up if they give in. I suggest buying sillicone earplugs for your family, as this can take a few weeks of consistency before it works (because remember, so far, your bird has been able to keep your attention this way, and when it suddenly doesn't work, the behavior will seem to get worse before it gets better, but that is called an extinction burst and it's normal).. It is very clear that your bird is doing this for attention and you also have to teach them to play with toys if they don't seem too interested (model yourself playing with it, lots of attention and treats if she shows interest in the toys etc.
You can PREVENT screaming in some cases by talking to your bird from the other room BEFORE the screaming starts.
Another thing-- if you walk out of the room and she DOESNT scream right away, come back in and praise her for being good and quiet. Try to see if you can gradually be out of the room for a few seconds longer over time and keep popping back in BEFORE the screaming starts and praising..
I will ask more questions about the flying attacks later, because I have a feeling it also has something to do with attention...If she sees you leaving or walking away and flies to bite you, you are forced to stay in the room a bit longer, touch her etc...I'd stop putting her on her cage and try a time-out stand or the floor and the "shunning method". I will try to post more on that later.
You are creating a monster. This can't go on for 80 years...Think about it, if you spoil this bird and never teach it independence or to eat on its own etc, it is going to self destruct when you have to go to work someday or when it has to be alone...Plus, you can't sustain this, and if it gets worse (as it will unless you resolve to teach independence) then you will likely end up with a bird that you cannot tolerate and when re-homed, your absence (due to this lack of independence and due to this shoulder feeding habit etc) will be a nightmare for anyone else...because it is already bad for you, and your bird hasn't even hit puberty..
I know screaming from a U2 can make your head feel like it is going to explode, but you have to let her scream sometimes.
Gun-range noise-blocking headphones will make it easier to ignore the screaming when it starts, but don't leave anything you need in that room because if the screaming does start, you CANNOT return (even if you need your keys or phone etc) until the screaming stops..
These also are good.