Hi Alexia,
Don't give up yet! I, too, have a rehomed 'tiel who came with her clutchmate. Their owner did nothing with them and said they were "mean birds". It was necessary for me to separate them because the male, Tico, was brutalizing the female, Teyla. When I did separate them, they both SCREAMED for each other incessantly! I had to place them in the rooms farthest apart and close the doors. I was at wits end. They had only known each other and had never been given the opportunity to socialize with humans. I eventually found another loving home for Tico. I still have Teyla and for quite a while, she still screamed for no apparent reason.
It took a few months for Teyla to get interested in humans and not bite or hiss. BTW: my worst bite came from her when I attempted to grab her from a dangerous area. She bit me sooooo hard it not only drew blood, but also, damaged the nerve in my finger and she would ~not~ let go! Early on, I did the same thing you are doing by placing my hand in her cage to get her to tolerate it. She would hiss, nip, and run away. She wanted nothing to do with humans. I was so desperate that I talked to a breeder friend of mine who had very valuable advice which I followed.She is such a different bird now!
I started by working with her out of her cage on a T perch in the bathroom (with commode lid down and room door closed). Yes, I had to chase her around the cage with a hand towel to grab her and then place her, screaming all the way, into a travel cage, just to get her into the bathroom. The cage is ~her~ territory, which is why we needed a neutral place to train.
She originally took no interest in taking any food from me. So the best I could do was simply praise her in a calm tone whenever she did good. I did find that she liked millet when I put it in her cage and left it for a couple of days. So, I continually had millet with a very long stem to offer her while training. At first she had no interest in it. Now, she looks for it!
The first thing I trained her to do was step up. I wore very thick heavy leather gloves while I worked with her so it wouldn't make a difference if she tried to bite me. She learned very quickly that she couldn't hurt the hand in the glove. She would hiss at it but still get on my finger. It didn't take long before I didn't need to use the gloves anymore.
I also used one of her old tail feathers to pet her with it (while announcing, "Mommy pet.") If she bit it, no problem, she wasn't going to do anything to that feather that I was going to feel. She learned that being touched wouldn't hurt her. We are still working with this.
As for the hissing when my hand was near her in the cage, I was able by then to have her take millet from me ~if~ she was at one end of the very long stalk and I was at the other end. From here, I would put the millet up against the bars of her cage and let her come to it and eat some through the bars with my fingers pushing it against the bars sideways (like 1/2 inch away from her). Once she got comfortable with me doing that. I held it inside her cage and waited for her to come to it to eat some. I steadily made sure there was a shorter and shorter stem and now she doesn't mind if my finger is touching her wing as she's eating it. Just today she even put one foot on my finger as she ate it - this was a first. Bottom line is not to chase them around but to let them get comfortable coming to you.
Now, as for her screaming: she will scream if she hears Crows or Blue Jays and she will scream when she want's to go to bed (and have her cage be covered up). Every few days she may scream if she is looking for us and don't know where we are, but, this doesn't happen much and she will be as quiet as a church mouse if I whistle at her or talk to her or go into the room where she's at. What she does now is very bearable.
So, IMO, why your baby is screaming right now is that he has not bonded with you yet and is screaming for his prior 'flock'. Get him to bond and I think he will be just fine.
I have found the the more socialized I was able to help Teyla be, the less she screams. She no longer hisses at us. I can take her for a walk around the house (stopping to reward her with millet for staying on my finger), she steps up for me and my husband without problem, etc. She is now a very active part of our flock.
So, be patient if you can. Work with your baby and I firmly believe he will come around.
Let's us know how it's coming along.
Good luck!
Deb