"to feel comfortable in one's own skin" It's hard to find an expression that matches it perfectly, but here's some ideas. Ex: "I felt comfortable in my own skin for the first time" 1) 난 처음으로 나 자신이 거추장스럽지 않았어 (거추장스럽다: be in the way, hindering) 2) 나는 처음으로 내 정체성을 찾은 느낌이었어 (정체성: well grounded sense of oneself) 3) 나는 처음으로 나를 찾은 느낌이이었어. 4) 나는 처음으로 내 자리에 돌아온 것 같았어. #1 is probably lighter in meaning, emphasizing the "right feel" about oneself. #2 through #4 all have the sense of "finding one's inner self and feeling more confident than before toward the world".

to be comfortable in one's own skin : 자신에게 만족하다 ex) happiness is accepting who I am and being comfortable in my own skin → 행복은 나를 있는 그대로 받아들이고 나자신에게 만족하는 데에 있다. you can just say it in korean natually "나한테 만족해"