You are NOT the only one!
I used to work (well, unpaid) in an undergraduate lab. I would run these tests then upload the data to graphs and submit them to my supervisor... except sometimes I had the wrong data! (Yes, it happened more than once). Which is a BIG no-no in the world of science. Also, my boss made me feel really bad about it.

Mistakes happen.

Also, you should take your parents' encouragement to apply to jobs as a sign that they trust you to take on those responsibilities!

I totally get where you are coming from, though. I often beat myself up at work for little mistakes I make, or when I get behind on tasks. But it's all in my head!

How old are you now? I imagine that other job is so far behind you now that it doesn't matter. NO ONE is grumbling about the mistakes you've made. Sorry you're going through these feelings, it's just a matter of changing that self-perspective. Give yourself some love!