Finger nail seperation. Rettach to nail?

Hi. So, as you can see my right finger nail before and after images. Left one is recent and right one is 1 week old pic. Actually, a one week ago, I was cutting my nails but unfortunately my right finger was cut in a wrong way that its corner wasn't cut properly. So, I left it grow it again. So after 2-3 days it started hurting whenever there was pressure like nail is trying to pierce in the corner. But somehow..pain got better. Then I noticed that right upper portion of nail where it was hurting..turned a little darker than regular pink..now yesterday I saw a white thin skin which was probably a sign of fungal infection if I am not wrong. I pressed that corner of nail and I saw a little drop of white pus and whipped it off. Just to be safe, I used betadine on it. But today I noticed the corner skin was harder than normal which I peeled off as you can see in pic.But now I also see that that dark pink/purple corner nail turned white today as u can see. so, will nailbed rettach to nail?