Did I handle this correctly?!

Did I handle this correctly?

My brother came in the house screaming from a huge splinter. I mean a HUGE splinter the diameter of 2 toothpicks. To give you an image... imagine a tooth pick in a tunnel and the tunnel made of skin and the toothpick the splinter. The skin on top was a clear white color so i knew it wasnt deep. The splinter was embedded in the underlying skin though, so pulling it out was not an option without further embedding it and tearing skin. So.. I took a knife (sounds barbaric but it was the only thing sharp enough)and cut the roof of the tunnel (the whiteish clear skin which didnt hurt him) and freed the stick.. now he just has the wound where the splinter was laying on his skin. Did i handle this correctly?? We dont have any alcohol or peroxide... is there a subsitutei can use to clean out the wound? My other brother had the idea of sticking the wound in the pool to clean it out (chlorine) does that work? As soon as i get to my moms house we will properly wash it and use more band aids.

3 weeks ago
my dad stepped out for the moment.. so he was not around. I am 15 by the way and not a stupid idiot who doesnt know what they are doing.

it should be fine. just run it under some water (skip the pool this time). when you get somewhere with better supplies clean it out with some alcohol or peroxide and then bandaid it.