S.H.
If you go to your local bank, they often can create an account, for donations etc. for this.
I have seen this in my own city.
When a family like this, has a child with dire health, they put an ad in the local newspaper, and/or have tv media coverage about it. Then the newspaper ad or tv news coverage about it, will say... that "Donations are being accepted via 'ABC bank'..." etc.
And then, in tandem with this, you would have a website. Don't know how it is then created so quickly. Or do FaceBook for it etc.
The website would need something like PayPal, to accept money for the site etc.
You would ALSO have to, consult with the Bank or Tax professional, about how to set it up, being it is a "charitable" entity which receives money for a certain purpose.
I would ask a bank.