Quick format vs full format
A quick format creates a new, empty file system index. The old data usually remains on the disk until it is overwritten, so recovery is often possible. A full format on modern Windows writes zeros across the disk, which normally makes recovery impossible.
What reduces your chances
Copying new files, reinstalling an operating system, or creating new partitions on the formatted drive overwrites old data. The less the drive is used after formatting, the better.
What you should do
Stop using the drive, note exactly what was done (format type, tool, file system), and contact a professional. Do not run multiple recovery tools that write to the same drive.
Important: Switch the drive off if it makes unusual sounds. Stop using the drive immediately.