I finally was able to organise our drawer today. It was easier than I thought it would have been. I only used these boxes:
As you can see, they are just cardboard boxes that previously contained baby's nappies. I just measured and cut to the desired length and placed it on the drawer on how I'd want to look it and became like this:
It's really easy. You don't need any complicated contraptions whatsoever. Now our drawer won't be a mess every time we get something from it.