I don't think there is anything special about the verb "sentir". "Sentirse" is just using it in a reflexive way, and the same holds for many other verbs: acostar, cepillar, duchar, levantar, etc.
Was going to say exactly this. Nothing out of the ordinary here. OP appears bilingual but must not spend much time translating between languages. You will face such problems (maybe they can be thought of as an example of an impedence mismatch [0]) whenever going between languages, especially when you're crossing language families.
