Measurement of an inductor not accurate at all
First of all, you should be measuring the voltage across the resistance. 
Because you want to know the current that is flowing in the circuit. 

\$ V_R = \sqrt{V_S^2 - V_L^2} = \sqrt{5.12^2 - 2.56^2} = 4.43V \$

Hence the current is \$I = \frac{4.43V}{100\Omega} = 44.3\textrm{mA}\$

The inductor reactance is \$X_L = \frac{2.56V}{44.3\textrm{mA}} = 57.9\Omega \$

And finally \$L =\frac{X_L}{2 \pi F} = \frac{57.9\Omega}{2 \pi \cdot 91\textrm{kHz} } = 101\mu H \$ 

As for your equation, the correct one is:

$$L=\sqrt{\frac{1}{3}}\frac{R}{2\pi f} =\sqrt{\frac{1}{3}}\frac{98\Omega}{2\pi 90 \textrm{kHz}} = 100 \mu H $$

And this equation is true only for a frequency at which the (Vgen/Vinductance) = 0.5