Tiffany, did you make any changes in the household at the time this behavior started, a lot of the time a change triggers such behaviors? He also might think he has to compete with the two loud children for attention, if it works for them then he figures it will work for him too.
I know this is frustrating for you and you responding to his screams is only making it worse, the attention is just causing him to do it more, you are rewarding bad behavior.
How much out of cage time does he have every day, maybe he does not get enough time?
Please do not consider rehoming him at this time, lets work on trying to find the cause and put a stop to it or at least reduce the amount of it. Some of the other members with more experience than I might have some suggestions and ideas that will help you more than I can. Just hang in there, help is on the way.