the Federal Reserve was established by the Federal Reserve Act of 1913. It was created mainly because of a series of financial panics like the Panic of 1907. It addressed financial instability, inelastic currency, and a need for a lender of last resort to prevent bank runs. The Fed was created in secrecy during the meeting in 1910 at Jekyll Island, Georgia. There were a few reasons for the secrecy one was because public distrust of big banks, that being the public resentment toward Wall Street bankers. the other reasons for the secrecy was political sensitivity and preventing sabotage by meeting in secret at a remote private club so participants could hammer out a complex compromise between different banking interests.
You nailed it with why it was created and why it was secret. Mainly to avoid public backlash and increase the chances of passing the banking changes. Some debate that it could also have been in secret because those powerful bankers wanted to create something that would ultimately benefit them, without other people really even getting a say.