Shortly: the battery should not have been damaged at all. Continue using your new adapter.
First, current mismatch is not as dangerous as a voltage mismatch because internal power supply in the laptop is sensitive to overvoltage, but when external adapter could not provide current neccessary for laptop's operation it will just turn off and drain battery instead as if adapter was unplugged.
Second, there are many levels of conversion and protection between your power supply and the battery cells (by writing "cells" I mean the thing in the battery unit that gets charged). There is internal protection in the battery that continously monitors voltage, current and temperature of the cells and handles overcurrent, overvoltage and many more erroneous conditions. Also, battery don't get charged straight from the adapter: there is at least one chip, the charge controller which not only internally stabilizes it's output voltage but also has it's own input protection. So if everything had worked and keeps worked, your laptop is very unlikely to be damaged.
Now you cannot work without adapter plugged in because it's output current was only to power the laptop and not charge the battery. Moreover, in peaks of current consumed by laptop it even drained your battery because adapter itself could not meet even minimal current requirement.