We aren't really attacking you, just trying to find as much information as we can in the hope it might shed some light on the problem. Colin thinks it is an internal growth, and this is not caused by the water or the tank, but we needed to eliminate those as possibilities.
There is an awful lot of mis-information out there on bettas. For example, I'm sure you've read/been told the one that in the wild bettas live in puddles; they don't. We are also concerned that your other betta is not a victim of any mis-information you may have come across and want the best for your fish.
It is distressing for adults to have a fish with a growth like this, let alone a small child. Let us help you make sure your other betta lives a long healthy life.