Hi Patty,
I’m so sorry your cockatiel is doing this. It does sound like he is missing his mate a lot. I don’t know if they were a male & female, a breeding pair or how long they were together. Or how long it has been since the other bird died. It may just be a matter of time and he will adjust. If he is not too old, have you considered trying to get him another mate or companion? Or is this bird tame? Is the bird you put with him tame? But you said they end up fighting. Is the fighting severe? Some beak sparring and vocal arguments are normal, but I always say when the feathers start flying or blood gets drawn, it’s time to split them up. If these are harmless spats, maybe you can try leaving them together as long as you are around to keep an eye on them.
Generally it’s best to ignore screaming, because they normally do it for attention. In this case it seems to be related to the lost mate. If you can’t keep the other bird with him, try getting him a mirror. A mirror can be a great companion and there is no harm in it as long as he doesn’t get obsessed with his reflection – this would be if he starts regurgitating on the mirror, tries to mate with it, or spends all of his time in front of it rather than playing with his other toys or getting some exercise.
I do hope one of these solutions will help because it sounds like neither of you is very happy with how things are right now.
Thank you for asking Lafeber,
Brenda