"Inside" a boost converter? Do you mean the inductor current, the switch current, the diode/active rectifier current, the output current, the input current, the output filter capacitor current, or the input capacitor current?
Because there's plenty of different ones to pick from!
No matter what you do, you will want to insert a low-value low-inductance shunt resistor (SMD preferably) into the current path of interest, then probe that. If you're dealing with high-frequency and/or high-current converters, even a few hundred nH will massively skew your measurements, and your test leads + multimeter present much more than that.
As for "get the right voltage": Measure a DC current with your setup, say 1A, and look at the voltage you get. If you're actually right about the 5.9 ohms, you should see 5.9 volts across the meter, which is hilariously improbable if you're in high-current mode and don't have horrifically bad leads. Just use Ohm's law in any event.