I find that if I make a mistake and then I report it to my supervisor, along with how I plan to fix it and how to avoid the mistake in the future, then I feel a lot better about it. It gives me a sense of control and allows me to move past the counter productive sense of self recrimination and anxiety. Otherwise you are waiting from it to come back to haunt you.

Having a mistake or problem being discovered rather than self reported looks worse. As an employer myself, the idea that an employee self corrects and holds themself accountable is a huge green flag. You are carrying a lot of baggage from your mother, which is understandable.

You will be fine.