都可以.
let me through中的through是介词,用法类似于let me in,let me out.等
let me get through是let后加省略to的不定式的用法.它不仅有“让我过去”的意思,还可能是其它引申的含义.比如：
It's your love that let me get through the miserable days.是你的爱让我度过了那段悲惨的日子.
My Lord,please let me get through the graduation oral examination.老天啊,请让我通过毕业口语考试吧