How to recover an overwritten iPhone back up?

I had my iPhone restored at the Apple Store yesterday as it had been acting funny and crashing a lot. Before my visit there, I backed up my phone to iTunes and had a backup for the phone before it got restored. At the store, an Apple employee told me that it would be unwise to restore my backup as he thought something on there was the source of the problem. I agreed to not restore my backup onto the phone to see if that was causing the problem.
However, when I got home I plugged in the new, restored iPhone into iTunes and it's backup overwrote the one from when it was previously backed up. To make things worse, I'd even ticked the box in iTunes where you choose to not synchronise the phone automatically, yet it still deleted my previous backup and replaced it with the new, blank one. Now, I'm absolutely furious as I wanted to keep my old back up as it had all my notes, my reminders, everything on it.
I want to know if there's ANY way to recover a backup that has been replaced as I'm absolutely gutted and I need my old backup.

Added (1). I should probably make it clear that my iPhone has been wiped so I can't use programs like Wondershare to recover files from the phone or iTunes as the back up I want has been replaced.

I think you should not use you iPhone from now on until you get your things back. Now what you need is a tool that could help you to recover your data directly from your iphone or extract stuff from your itunes backup files. So that you could get your notes and reminders back.
Try http://www.ios-data-recovery.com/, called the world's #1 iphone recover. I have one but I hardly use it.