Are there any cooler/better-matched/modern phrases to express that you have to recover your own fault or make up your own mistakes by yourself? I found the phrase in title by search, but I guess the meaning is slightly different.
We often say "clean up your own mess" to convey that the author of a bad situation has a duty to correct it, and not expect others to do it for him or her.
In common, modern parlance, you will hear you reap what you sow. Another common expression equivalent in meaning is simply (all) actions have consequences.
You reap what you sow per the ODE means "you eventually have to face up to the consequences of your actions", not that you have to recover on your own or whatever.
The modern version of this phrase is "what comes around goes around", karma would be a synonym, and of course the phrase itself comes from the Bible.