Are the characters for sleep and feel the same?
Chinese characters can have multiple meanings and multiple pronunciations. You figure out the intended pronunciation and meaning based on the context. In the context 睡觉 （Shuìjiào，"go to sleep"), the pronunciation is jiào and the meaning is "(a period of) sleep". In the context 感觉 （Gǎnjué， "feeling"), the pronunciation is jué and it contributes the meaning "feel".