Battery needs replacing, short in the plug, randomly turning off

My problem began as I plugged my MacBook Pro purchased in China into a plug ran through a voltage converter in Malaysia and it shorted out causing the top of the plug to turn black. I had been using that method for a month and never had a problem before that. I examined everything and all seemed fine. A couple days later noticed a service battery warning , a week after that, a replace now warning.

The computer says I can use without damaging the computer but now it started turning off even while plugged in. I can’t get a new battery because I live on a small island with no Apple store and can’t leave for a month. I need my computer but I am worried that this might be harming something more serious than the battery.

Help