Feelings are facts. "I feel frustrated" is a real feeling — and a fact about your feelings that you can state (if that is the case). The "feeling of knowing" is just a feeling, though; it says nothing at all about whether what you "feel you know" is true or not. That requires empirical evidence and rational logic.
yes indeed! important point. Feel happy, sad, fear, joy, - valid statements. I feel that the table is in the wrong position, is too high. Feel that it is too expensive. Feel that it is too fast.
Use of word 'THAT' whether real or implied signals a confused use of 'feel'. Confusion betwen thinking, and feeling, is deep at the heart of a dysfunctional culture.