You need an oscilloscope to do this properly, since you'd probably like to know the magnitude of ripple sitting on top of the DC output of the boost converter.
BUT... you also need to realize that the supply voltage is the property of the power supply, but the _current_ is the property of the load resistance. In other words... say your power supply is providing a solid, regulated 3.3 volts and isn't current-limited internally. The current through the circuit will then be determined by Ohm's Law using the resistance of the load. I = V/R.
Now... with LEDs.... these are very non-linear devices. The LED specification will have a "forward voltage" Vf which is the voltage drop across the LED at some small current. If you supply more voltage than this, the current through the LED will go up. And different kinds/colors of LEDs will have different Vf values. So your LED is drawing whatever current it draws at 3.3 volts.
The "100 mA" rating of the boost converter is the rated maximum current output when the supply voltage is 2 volts. This does not mean that it will always push 100 mA through whatever load ! The _load_ determines the current draw at a given supply voltage. Also, when you use a DMM as ammeter, you are putting its shunt resistance in series with your circuit, so this will actually affect the current as well. For measuring very small currents, I think it is generally better to look at the voltage drop across a small Current Viewing Resistor in series with the circuit, like a 0.1 ohm precision resistor. The voltage drop reading across this resistor will be converted to a current reading by Ohm's Law, I = V/R again.
What is the Vf of the LED you are using?