The accepted answer is simply wrong.
It is probably from a Chinese folk tale since it claims to be Chinese. I daresay I have read similar folktales, especially the swallow-the-bead-and-turn-into-a-dragon part, when I was a kid. I cannot figure out the exact one. But it is easy to search out folk stories with similar motifs.
e.g. https://book.douban.com/subject/11633147/
一个叫阿宝的孩子拾到了一颗红色的宝珠,他把宝珠放进米缸,米缸里立刻盛满了白花花的大米;他把宝珠放进钱罐,钱罐里立刻填满金灿灿的钱币。阿宝用这颗宝珠帮助周围的邻居都过上了好日子。奇怪的是,自从阿宝捡到这颗宝珠后,天上就再也没有下过一滴雨,大地干涸、庄稼干枯,乡亲们愁眉不展。
一天晚上,阿宝在梦中见到一条雨龙在空中喷雨,醒来后,他决定动身去寻找这条雨龙。一路上,阿宝帮助了巨蛇、梅花鹿、鲤鱼和苍鹰,每个动物朋友都赠送了他一样礼物,并警告他要当心一个叫红鬼的妖怪。随后,阿宝果然遇到了红鬼,并从红鬼口中知道了自己手中的珠子叫龙珠。为了保护龙珠,找到雨龙,阿宝果断决绝地吞下了珠子。最后,在动物朋友们赠送的礼物的帮助下,阿宝变成了一条会下雨的龙,把甘露洒向了人间。
沙县民间故事
This story lacks the part of the magical power of the dragon bead, but retains the part of swallowing the bead to become the dragon.
https://www.sohu.com/a/349852173_488223
This one is rather long, but the story is almost the same, which is easy to find if you can read Chinese.
A further question is whether this kind of folktale has a origin in Classical Chinese literature.
And I must say many Chinese folk tales have a style and sentiment that you won't find in classical Chinese literature. Not to say even China proper is a country that comprises several distinct territories, varied cultures, and peoples. It is always hard to say what is really "un-Chinese".