Being self-conscious about an audition like this, especially a singing one, is normal. A lot of people are scared that they might not be perfect with their performance, singing or speaking-wise. But the thing is, when auditioners start thinking in terms of "was my performance good, could I have been on pitch" rather than "did I play this character to the best of my ability," it shows. You don't need to worry about whether or not you did a good job - the worst I can do is not cast you for the part. Just do the best job you can, and be proud of it. Thanks for auditioning!