Li-Ion charging indicator

I want to make a charging indicator for my power bank(Actually the power bank has its own indicator but unfortunately after I install the battery in my system it gets hidden). Hence I put a 1ohm series resistance in charging path and used its two end as differential input for lm393p comparator. The circuit is attached herewith. Somehow the indicator does not glow. On the input pins I am getting 0.2V of difference between + and - pins yet the output is low. I changed the series resistance from 1ohm to 1kOhm(Just for sake of testing as it reduces charging current considerably) and circuit works perfect. I am perplexed as to what could be the possible glitch in the circuit.

The inputs of an LM393 do not work if their voltage is near (within 1.5V) from the positive supply voltage as shown as its Input Common Mode Voltage Range on its datasheet. Your inputs are very close to the positive supply voltage so of course they do not work. But the inputs work perfectly near ground so the current sensing resistor should be in series with the negative terminal of the power bank and ground. An LM393 has a maximum input offset voltage of 5mV which might cause the LED to still be lighted when the charging current is zero so the grounded input should be a few mV positive with two resistors as a voltage divider to correct it.

You have 2k ohms in series with the LED. If the LED is a 1.8V red one then its current will be only 1.6mA which is dim. If the LED is a 3.5V blue one then its current is only 0.75mA and it might be so dim that you cannot see it.

Why short the LED to turn it off? Instead why not have the output of the LM393 going to ground to turn it on? But its output current is fairly low at 10mA.
Do it like this: