Does the phrase "I take myself with a grain of salt?" mean "I think about myself sceptically"? Or it doesn't? Either the first phrase have no sense at all?
It means exactly that and you can use it, but it's not normal to use'I' in this expression. However, that's the beauty of English! If you change a 'normal' expression slightly, you add humour, emphasis or emotion. This device is used by creative writers all the time. You might use this when talking to some friends about the new exercise program you have decided to begin. "I'm going to start running everyday in the morning. However, I take myself with a grain of salt." Most English speakers would 'get it'. I hope that helps.