You're certainly right about people being very critical, but ultimately it stems from all of us being concerned for this bird, and we want OP to know that they are doing the wrong thing by not getting professional medical help for it. I think everyone does need to dial it down a bit, by now OP knows to take it to the vet. No amount of hassling them is going to increase OPs likelihood of taking it to a vet (unfortunately). But we need to remember that OP evidently cares for the parrot and is doing a lot of things right, including reaching out for help.

HOWEVER, the notion that "what happens... happens" kind of went out the window when OP picked the bird up in the first place. As far as I am aware, most places encourage injured wildlife to be taken to a sanctuary/hospital, and if neither of those are available then a vet is the next best thing. In picking the bird up, by not doing this and keeping the bird in their own care they are doing the wrong thing by it. Furthermore it has been pointed out that the bird likely has an injury in its right wing, so it's not going to get better in OP's care alone. The invasive species comment is true, but again OP has decided to pick this bird up, and so has become responsible for it, and the best course of action is to get it medical care.