You cannot hear your own voice the way that other people can hear it. The sound travels to you from inside as well as outside, the brain receives a whole lot of resonances that do not 'transmit'. So it is essential to find a coach with ears that you can trust.
The essence of singing lessons is that teachers 'listen' to their students and comment on what they hear. They praise, give advice, suggest different ways of overcoming difficulties, encourage, but above all they listen, and listen hard.