Better yet, "I recently lost weight but I don't like how skinny I look." or "I'm losing weight these days but I don't like how skinny I look." You don't typically use "these days" for something that has already happened. Use present progressive ("-ing" form).

You'd say "These days I lost weight but I don't like how skinny I look." "my skinny appearance" is ok but "how skinny I look" is more typical. "I don't like my skinny look" is awkward. Also "I lost weight". "I lost my weight" is incorrect.

Same meaning. Your look is your appearance.

It would be helpful to have a sentence for context. In definition they both mean the same thing but context can change the idea conveyed.

I think they mean about the same thing. Would you give an examples of use in a sentence?