Yes, the verb "чувствовать себя" requires instrumental in the examples as follows:
Я чувствую себя героем. - I feel like a hero.
Я чувствую себя космонавтом. - I feel like an astronaut.
Я чувствую себя больным. - I feel ill.
Я чувствую себя обиженным. - I feel hurt.
etc.
Literally, this expression is something like "I feel myself to be...". The verb "to be" (быть) requires the instrumental: "быть героем", "быть больным" etc. The same is true for "чувствовать себя".
BTW, it is a very typical mistake Russians often do when speaking English. They use "I feel myself" expression. For example, if you are unwell, we usually say: "Я плохо себя чувствую". Russian people tend to translate it literally into English: "I feel myself badly"