The -in suffix for marking a female profession or association to a kind or group of females is a bit tricky to use. The indefinite article isn't involved in this, though.
Ich bin Europäer.
Ich bin Europäerin.
As a woman you can use both of these and you are correct. By using the -in suffix you only add the information telling everyone you are a woman is very important to you – people will draw their conclusions.
Sie ist Europäer.
Sie ist Europäerin.
Both are as valid, though the latter is more common.
Das sind Europäer.
Das sind Europäerinnen und Europäer.
Both are valid, but only people with a stick up their … spine use the latter one. It's just too inconvenient.
About the use of the indefinite article:
Ich bin ein Europäer.
Ich bin eine Europäerin.
Again, both are as valid. The difference to the example without the indefinite article is subtle, as the use of no/indefinite/definite articles tells apart kinds from identical items out of a group from certain items, and in this example, kind and group Europäer are identical on a semantic level. This is often the case.
You have to make up more specific examples to see the difference:
Sie ist Lehrerin von Beruf.
Sie ist eine Lehrerin unter vielen.
Sie ist die Lehrerin meiner Deutschklasse.
Sie ist die Lehrerin, nicht eine der Schülerinnen.
German doesn't make a difference between the indefinite article ein ("a") and the counter ein ("one"). This sometimes confuses learners. Take ein as a matter of last resort, when you don't have multiple items to select from a group, and you don't want to select a specific item either. You use "one" then – ein.