welcome!
1. You have hardly had her long enough to build trust....
Does she like you when you are around??
If she likes you sometimes, apply the following (if she never likes you in the room, disregard)
You are assuming it is not for attention....How do you know? An extinction burst is common when a behavior is ignored (aka, put on extinction). You may also be attending to the calls without realizing that you are...even talking about it or looking at her is attention....I'm banking on attention and lack of patience. You MUST wait it out....sometimes 8+ hours (over more than 1 day) and make sure you call before it starts to prevent it when you leave the room (along with using key phrases to increase the parrots anticipatory set--e.g, "going to work" (if gone for 6+ hours, "going to the store if a short trip under 2" etc etc). It may also be attention for a certain person, or a desire for attention ON HER CAGE (not elsewhere). She may not want you touching her-- just in her line of sight. You can't assume it's not attention, especially as I have a hunch this bird may be hormonal on top of everything. You say "even leaving the room" but that is like..step 1....It's not extreme...If you look at her, enter to grab your phone, talk louder because she is screaming, etc etc (that is ALL attention).
Did you move the cage or is she in sight of a window? little changes can scare them and cause screaming...there is just so much that could be going on here, AND it can be normal l to have a screaming bird when needs aren't being met or behavior is misunderstood---you are the one who chose the bird. Now you find a solution other than re-homing (something good for the bird). I am glad you are here and I hope you are able to trouble-shoot.
How many hours of sleep is she getting on a schedule in a dark and quiet space nightly (again, schedule is key)?
How do you pet her when you do? (anywhere other than the head and neck is sex and will amplify nasty behaviors)
How much access does she have to huts/tents/boxes/bedding/shadowy spaces (in or out of cage)---shadowy (even a little shadowy) is bad and will amplify hormonal behavior--best to cut it out totally.
How is diet?
How many hours is she out per day?
Please read this entire thread (my responses are pretty much what I would say to you-- there are a few of them and you should read them all:
http://www.parrotforums.com/amazons/89749-amazon-too-attached-me-hates-my-family.html
http://www.parrotforums.com/conures/86786-need-help-bird-upsetting-whole-family.html
Thread on ABA (applied behavior analysis)-- see my replies-
http://www.parrotforums.com/questions-answers/89733-new-parront-here-biting.html <--read for detail
I have a feeling this is a combination of attention and anxiety etc...possibly wanting you around but not trusting you enough to be on you. You can't fully rule out your role in attention just because she is flying back to her cage. It is so soon for her to be trusting you fully, but she is probably feeling vulnerable and scared alone...
You need to make her feel safe and comfortable... do not push anything (including pushy things like, toweling, shoving food in her face, hanging your arm in the cage etc). Move at her pace, but respect the fact that she needs a flock (even if she isn't your biggest fan yet--- you need to be around).
..but BEFORE the screaming starts...not after