Even though a tumor may appear on the outside of the body it's quite often because of an inside condition.
This could also be something relatively simple like a 'feather cyst', but either way, she will need professional intervention to not only diagnose, but treat.
You're doing a very good job with the special care and smaller cage so keep it up. Using a more gentle saline solution, like what people rinse contact lenses in, may be a good choice over salt water which has an abrasive quality.
You can also use just plain clean water until you have her seen.
As with all things that might go wrong with our feathered friends, early intervention gives us a better chance at keeping them around a bit longer. Your 'tiel should have an average life expectancy of 18 years and these days it's not at all unusual to find 'tiels well into their 20's.
Blood chemistries and X-rays should be expected (and encouraged).
I think you're mostly second guessing yourself because you're worried, but trust yourself! This 'tiel didn't get to be 14 years old without exceptional attention. Let's go for another 10 years or so.
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You remain responsible, forever, for what you have tamed.
