A sense resistor in the range of 1/20 or 1/10 ohm ought to develop sufficient voltage across it, so you can easily amplify it with an NPN operated in common-base mode.
Voltage gain is high. This arrangement is not so well-known as the typical ways of using a transistor. It may require some effort to make it work properly.
Notice none of your led current passes through the transistor itself. The relative B-E voltage is altered by current going through the sense resistor.