>Estonia is a member of the EU, and is therefore bound to use the Euro and only the Euro as its national currency
Just a nitpick, this statement isn't quite true.
>Nine countries (Bulgaria, Croatia, Czech Republic, Denmark, Hungary, Poland, Romania, Sweden, and the United Kingdom) are EU members but do not use the euro. [1]
The term you are looking for is the Eurozone rather than the EU.
[1] https://en.wikipedia.org/wiki/Eurozone#Future_enlargement