So we have a happy ending to all of this, last night I posted in the app called nextdoor that we found a lost cockatoo. A woman named Kristi replied back that she might know whose bird it is, Kristi is a manager of a trailer park that sits a few miles to the South of my grandmother's house. Kristi said the woman that owns this bird is named Carol, Carol is elderly and does not have a working phone apparently, everybody in this trailer park knows this bird apparently and has been looking for it and posting flyers up. The bird is named Rose and has been missing since Monday. Carol's son is named Shawn and he always walks around with the bird on his shoulder with no issues until Monday.
On Monday the bird took off from his shoulder and they could not get it back. So Carol has been devastated and Shawn has felt really guilty since it was his fault the bird got away. My mother spoke to Shawn since Kristi gave me his number and he sent us a picture of the bird with his mother Carol and also the band number he gave my mother matches the one on the bird so we know Carol is the legit owner.
The woman that lives across the street from my Grandmother is named Tammy and she has been taking care of the bird since yesterday since she owns another exotic bird. Tammy will be taking the bird down to Carol later today to reunite the bird with its owner. So thanks to the nextdoor app we have a happy ending.
Shawn sent us a picture of his mother Carol with the bird, I'll attach it to this post. Thanks all for your help!