Should I be concerned?

So had a splinter. Got it out, but there is like a little speck of it still in there like very tiny. I tried to get it out, but couldn’t get it cause it’s so small. So I soaked it in hydrogen peroxide and now put neosporin on it and a bandaid. Will it be okay should I be concerned? Sorry I just really hate splinters and my finger hurts from poking at it