How we sound to ourselves, even listening to something taped, is not how other people hear us. Too, their perceptions of us as someone else also change how they hear our voice and "see" us in ways we cannot get because we are stuck being ourselves with our own experiences of us, etc.
I would talk to your T about how you feel about your voice, ask her how she perceives it and brainstorm ways you can practice correcting some of the little faults like using too many fillers, etc. My husband has a good line he uses on me, "I don't hear any nouns!" which gets me to stop what I am saying and think it through more, get a complete sentence going, LOL. I get excited and trip along merrily, flitting from subject to subject with no references and lose my listeners. My T obviously agreed with that as she asked could she borrow my husband's line