Given its age its possible your battery has just died. At this point you’ll need to find your way to someone with the deeper skills and access to a spare battery to test your system out.
At worse give your system enough life to allow you to backup your last few files to your iCloud account before giving your system its last rites if you want to move to a newer system.
Update: I guess I wasn't clear.
You would need a charged battery to offset the inability of the USB-C port from charging for what ever reason. Then you could quickly backup your data to the iCloud before the spare battery died.
To do it your self you would need this: MacBook 12" Retina (Early 2016-2017) Battery and here's the process Retina MacBook 2016 Battery Replacement
Frankly, I would find someone who has the battery who can quickly connect it long enough test your system and to do your backup Vs buying the battery.
Since you had issues with the USB-C port you might be lucky enough to just replace it! MacBook 12" Retina (Early 2016-2017) USB-C Port Assembly
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