Hello passionfruit: You know... from my perspective this is a case of "first things first", as the saying goes. I recall reading a previous post of yours regarding your having burned your fingers & wondering if you should see a doctor. You write here that your fingers have blistered & one of them feels weird... like you can't feel it.

My personal opinion, for what it's worth, is you need to "own" what you've done & see a doctor. But I also I know about the "lie" thing. I've done it myself in the past.

If you feel you have to have a lie, perhaps you could just say you spilled boiling water on your fingers.

Chances are the doctor's not even going to question it.
Personally I don't think you shouldn't be around kids with the injury you have. As your brother said, you can wear gloves. Or you can tell the children that you spilled boiling water on your fingers. They're not going to know the difference. But the greater issue here is that you seem to continue to keep doing serious harm to yourself. And that is something you really need to try to resolve. The question of whether or not you should read to kids is really beside the point, in my opinion.
Perhaps, since it sounds as though you'd really like to read to kids, you could make this a reward for seeing a doctor about your fingers. (I doubt that a background check is going to include finger prints.) Perhaps, in reading to kids, you can find something that can help you find a way to stop harming yourself. You would be bringing joy to the kids you read to & helping yourself to heal at the same time. Wouldn't that be a wonderful outcome?

I wish you well...