When you closed your notebook without saving did you have another notebook open? Or a Help page? Closing a notebook is not the same as closing a Mathematica Session. If you want to start over then close everything and start a new Session.
I just did two tests. I brought up an existing notebook, evaluated it and noted the last In/Out numbers. (50, 51, 52). In one test I saved it and closed it. In the other test I didn't save it before closing. These actions ended the Mathematica Session. I then started a new notebook and typed the statement 1+1 and evaluated it. In both cases the In/Out numbers were (1,2).
When I do development in a notebook I always use Sectional organization. Then if I end up in a rabbit hole I just start a new Section and delete the old Section and continue with the same notebook. Often I still want to copy over from the old Section. Sometimes I name them Try 1 and Try 2.
Another possibility for clearing out definitions is to use the old package CleanSlate by Todd Gayley. See: https://library.wolfram.com/infocenter/MathSource/4718/
Same answer as Arnoud Buzing
Another way is to go to "Preferences" -> "Advanced" -> "Open Option Inspector".
Search for CellContext and set the option from "Global" to "Notebook"