I caught my finger nail on my jeans and part of it got pulled back.
I snagged my finger nail when I was working in my garage, and part of it almost came off.
この場合、次のような言い方ができます。
ーI caught my finger nail on my jeans and part of it got pulled back.
「ジーパンに爪を引っ掛けて、一部がめくれた」
to catch one's finger nail on ... で「…に爪を引っ掛ける」と言えます。
to get pulled back で「めくれる」
ーI snagged my finger nail when I was working in my garage, and part of it almost came off.
「車庫で作業をしている時に爪を引っ掛けて、一部が剥がれかけている」
to snag one's finger nail で「爪を引っ掛ける」とも言えます。
to come off を使って「剥がれる」を表現できます。
ご参考まで！
カナダ 
