You're right. And your English is fine - we can understand exactly what you mean.
If the nationality begins with a vowel sound, the article should be 'an': for example, an American, an Egyptian, an Indian or an Omani.
But you need to be careful of two things:
1. Remember that this about pronunciation, not about spelling. So, even though 'Ukranian' and 'European' are spelt with vowels, they are pronounced with consonants ( 'y' sounds), so we use 'a' with these words. Likewise, 'Uyghur' is pronounced with a consonant sound ( like a 'w'), so you would say 'I'm a Uyghur'.
2. Not all adjectives of nationality can become nouns. Most of the terms which are both adjectives and nouns are the ones ending in 'n' and 'i'. Nationalities ending in 'ese', 'ish' and 'ch' can only be adjectives. This means that you can say 'He's an English man' (but not 'He's an English') or 'She's a Chinese woman' (but not 'She's a Chinese').
I hope that helps.