confusing current readings
Diodes do not follow Ohm's law. Instead, when forward biased they have roughly a constant forward voltage. For an LED, this could be on the order of ~2V to 3V though you should check the datasheet.

Assuming your circuit looks like this (you should include a schematic of your circuit to clear up ambiguities):







simulate this circuit &ndash; Schematic created using CircuitLab

Then the voltage across the resistor is \$V1 - V_D \approx 4V\$. Then using Ohm's law:

\begin{gather}
I_{R1} = \frac{4V}{R1} = \frac{4V}{200 \Omega} = 20mA
\end{gather}

Which is much closer to the reading you were getting. Further discrepancies can come from any number of sources:


I just roughly estimated \$V_D\$. You can measure this with another multimeter to figure out what it is.
Resistors have some tolerance. Again, measure the resistance before inserting the meter.
The multi-meter has a shunt resistor inside to measure current, and also has some tolerance. You can measure the shunt resistance with another meter, though it's possible the resistance is small enough that you'll need to use a 4-wire Kelvin bridge in order to measure it accurately. You can find the multimeter's tolerance rating on the box.


etc.