Formatting is data destructive. Don't do it.
In future I would suggest that you disable write-behind caching, or select "optimise for quick removal". This will minimise the damage from unsafe removals.
As for data recovery, I wouldn't trust any tool to write on your drive. Instead I would write any recovered data to a different drive.
However, before letting any tool loose on your drive, I would first examine the partition table (sector 0) and the boot sectors of each partition using a disc editor in readonly mode.
Which OS are you running?