Is "Cotton Industry" the proper term for an industry build around something more successful?

Solution 1:

It sounds like an eggcorn for cottage industry. Oxford English Dictionary, "cottage industry, n.":

2. In extended use. Any specialized enterprise or activity conducted on a small scale or in a loosely organized or unofficial way, either for profit or (now often depreciative) in pursuit of a particular group's own interests or concerns.

Merriam-Webster is more expansive:

1 : an industry whose labor force consists of family units or individuals working at home with their own equipment

2 : a small and often informally organized industry

3 : a limited but enthusiastically pursued activity or subject

You can see the difference if you search for news articles with the two terms. The "cotton industry" results tend to involve the literal cotton industry. The "cottage industry" usually involves describing informal or small-scale industries that might be done in the cottage, that is, at home.