'Pull your socks up,' at least in the US, would be an antiquated expression. My guess is it's more tied to school uniforms where the student has high socks visible as part of the uniform and not having your socks pulled up is viewed as being sloppy, ill-prepared, lazy, etc. In the US, school uniforms are very rare and have been for some time, especially in public schools. 'Apply yourself' is a very neutral, general, usable expression. It is less idiomatic. Other options are, 'put in the effort,' or 'do the work.'

Ian is right about the meaning of 'apply yourself'. 'Pull your socks up' is also a very common phrase, and is similar to 'apply yourself', but saying it suggests that, currently, you are *not* applying yourself. Therefore, to 'pull your socks up' means that "one should put in more time and/or effort" and/or "one should improve one's attitude towards a challenge or obligation (such as work or school)".

"Apply myself" = This is common. This just means to work hard and to focus on your task. "Pull your socks up" = Maybe this is a British expression? I never use this, unless I am truly putting my socks on my feet, haha. Good luck!