Wait, nope, i still don't understand. Is it possible to measure the current without knowing BOTH the voltage and resistance?
Well, yes it is - but not with a DMM. You can do this using an analogue meter movement. If the basic sensitivity of the meter is 50uA, then you can push through anything from zero to 50uA and it will give you the current. You don't
need to know the resistance or the voltage. Of course, since the coil of the meter will have some resistance, there will be a voltage drop across it, but you don't need to know either of these to measure your current.
However, if you want to use this meter movement to measure currents higher than 50uA, then you WILL need to know voltages and resistances in order to build the appropriate shunt circuit. Ohm's Law all the way!!
Or put another way: to measure either, voltage, current or resistance, you ALWAYS need to know the other two? Or is one ever enough?
With resistance, you have a passive quantity and you need to "excite" the component and determine its response in order to calculate that quantity ... So, yes, voltage and current are both needed. Always.
With current, you can - in some cases - measure it directly, but with
any sort of conditioning network, Ohm's Law is a must. In the case of a DMM, you absolutely need it.
Voltages are an interesting case and while there are some techniques that can be used to measure a voltage without using Ohm's Law, they are not the sort of thing you would see very often, if at all. So, in practical terms, Ohm's Law is applied almost universally.
The one overruling fact, though, is that if you cannot directly measure the value (as in the 50uA meter movement mentioned above) then you must have the other two values for Ohm's Law to be used. This is fundamental mathematics - whichever way you write V=IR (you can also see it written E=IR), there can ONLY ever be ONE unknown.