I've been having my own little dramas with pets and human ailments (I'm okay, I'm just having to deal with it all).
First of all, I've never had a bird that does the incessant shrieking thing, so mostly I have only read about it. I am dealing with a couple of rescue dogs at the moment who have issues of neediness and insecurity that is somewhat similar in ways to what your bird has gone through.
Having been neglected and not socialized until now, your bird is having some anxiety that your newfound bond is going to suddenly disappear. I don't know if birds have a longer memory than they are credited for, or whether once they learn a pattern it is harder for them to unlearn it, but either way, it takes a LONG LONG time to adjust. It is possible that they will never adjust (not what you wanted to hear, I know) fully.
Does the bird have any interest in toys? Lots of people say not to give the bird a mirror, but this may be a case where a mirror would be a benefit to the bird, in giving it another interaction.
http://www.companionparrot.com/articles/shoulder.html
Is it possible for you to set up a play gym next to where you are working, but that she can't get across to you and mix herself in with your paints? Really needy birds (like she sounds) almost want surgical adhesion to your body. I'm going through this with the dogs, altho the one I've had for 5 months is now able to actually lie on her bed across the room from me, and even allows me to get up to go to the bathroom without having to accompany me. But it has taken some doing.
I went that route with my Sun Conure to some extent, altho it does sound like you are having a possibly worse time of it. There are Bath flower essences for treating different types of fears. I'm not sure which one this would cover. I've used both aspen and mimulus for animals, as well as Rescue Remedy (which may be a good choice when in doubt. If it is not suitable, it simply does nothing.) The glycerin based version is harder to find than the alcohol based one, but it is available.
How high is the top of your bird's cage? How high (measured from the floor) is the top perch? How high to your eye level? Birds judge dominance as to who gets the highest perch. If your bird has a higher perch (in or out of cage) than your own eyes, this may be compounding your problem, altho with some rather dysfunctional birds I've worked on training (or retraining), it didn't matter that the top of their cage was waist level, they were STILL very hormonally driven.
And the hormones may be part of her problem. I often think of Tiels as being little Hormones On Wings, since it governs so much of their behavior. With a hen with a laying problem, this seems to exacerbate the problem too.
Is she still laying eggs? If so, how often approximately?
Diet -- this is a rough one. Part of the reason I have not been around is that I have been working with my sister and one of my former cockatiels, Gwinn, whose liver values just came back from the lab. Despite what one might THINK was a varied and healthy diet, he has values 100 times normal -- Fatty Liver Disease.
We are trying holistic methods with him, since there is little that alleopathic vets can do for him (indeed, his alleopathic vet is very interested in what we are doing and wants updates in case it works so he can use it for other patients).
Gwinn has been eating mostly bird bread (grain based) for breakfast, vegetables during the day, and seed at night, as well as some pellets. Part of the regimen that I am now getting my sister to switch him to is a change over to a sprouted grain diet for the amino acids, as well as other supplementation (milk thistle, dandelion, aloe) for his liver problems.
Fatty Liver Disease has many components, including heredity, that we can't do a lot about. And we're also facing the fact that none of us lives forever (altho we're doing all that we can to try and help him heal).
Your bird hopefully doesn't have this condition, but I am including a link that may help explain why it is that a seed-only diet is a problem, and a little bit of what to do with the diet BEFORE it happens to prevent it.
Fatty Liver Disease