touch negative and positive side of battery briefly
Normal battery packs have BMS circuit to protect it from short circuit and overdraining. You said the smoke came from the wire, which is mostly the result of the wires being overheated due to the short circuit current. Check your battery with a multimeter to see if you still get normal readings, most likely the battery should still work if the BMS circuit inside didn't get damaged. 

You added links of your battery, and that battery doesn't come with any BMS so there's chances that you might damage the cells due to the high discharge current during short circuit. 
If this is for personal project you can monitor if the battery is discharging at normal rate or if it's drained faster than usual to determine the state of the battery.

Battery datasheet