Selling an original t-shirt design to a fraternity I am not part of (copyright issues)

I tried searching for some answers before posting this but since my situation is so unique my questions were never completely cleared up.

So about a year ago I was approached by a member of a fraternity to design an original t shirt graphic that would include their letters, colors, and symbols (such as a specific bird and battle axe). I created a design that incorporated all these things but digitally drew them in a way that looks completely different from their traditional logo.

Keep in mind there was never an official contract or agreement, it was a very under-the-table kind of deal. He just wanted to surprise his brothers with a dope new t-shirt design for the semester.

I ended up spending way more time on the design than I thought I would, creating something I am very proud of. The original transaction with this specific chapter got postponed due to financial issues but I'm now starting to see the potential my design has to become noticed and sold on a much larger scale. Since the fraternity is a national organization with dozens of chapters and thousands of members and alumni, I would much rather target the larger market than just one New York chapter. I've already been contacted from another member in Georgia who came across the design on the internet and wants to use it for his chapter.

Here's where I'm lost. I have no idea how to approach this issue.
Am I even allowed to create an original design that uses a copyrighted name and sell it to frat members?
Do I contact the national headquarters and ask them purchase the file for them to print and distribute apparel?
Can I simply reach out to individual chapters by myself and see if they are interested in buying the design?
Is any of this even legal?

I want the design to get as much exposure as possible but I also want do it the right way.

One source I read said that all I need to use a copy written name or symbol is permission from the organization itself? If so, does that mean the fraternity's national headquarters? The president of a certain chapter? Some random brother who asked me to do it? You can see where it gets confusing.

I greatly appreciate your time and advice. Your opinion is valuable even if you don't know the exact law.
For specific names and details you can contact me directly at [email protected]