Determining inductance using a multimeter
Your calculation is wrong - sorry! The inductance causes a phase lag to the current. The impedance of the inductor for that reason can't add directly to the resistances The proper formula for the total impedance is

$$Z = \frac{V}{I} = \sqrt{(R+RL)^2 + (\omega  L)^2}$$

[Offtopic : This formula is easily derived by using the complex phasor calculus. That calculus is developed for AC circuit analysis nearly 125 years ago]

L must be solved from this equation. The result is

$$L= \frac{\sqrt{Z^2-(R+RL)^2}}{\omega}$$

This method is not practical if the inductance is small, say 1 mH or less.

For sub-mH inductors you must have quite high frequency to have well measurable U and I. You run out of the frequency range of your multimeter. Additionally: The stray capacitances make disturbing currents that bypass the coil and the skin effect makes the resistance of the coil much higher than its DC resistance.

Thus in uH range you should start to use for example LC resonance as the grounding of the measurements. Add a well known series C or a parallel C. Have an external diode rectifier for your voltmeter. You can find the resonant frequency and solve the L from the equation of the reaonant frequency. Even the stray capacitances can be solved by adding 1...2 new known capacitors.