Yes, I totally know what you mean. That used to be the case with me. But what got me past that was, paradoxically, recording myself! I mean, what you're hearing in the recording is only what everybody else is hearing when you sing or play in public anyway. The sheer horror of listening back to yourself repeatedly is eventually outweighed by the satisfaction of evenutally thinking 'That one isn't actually that bad...'

Violin playing is a whole other thing altogether though. I like to think I'm a reasonably good fiddler but when I listen back to my recordings it is a salutary reminder of how awful my intonation is. I've tried 'fiddle singing' once or twice and recording that has been useful to me in showing me I should never, on any account, try to do that in public.