You missing one, very important step. In order to get the impulse response of your filter while using the sweep sine, you must get the output of your system $h[n]$ to excitation with sweep-sine signal $x[n]$:
$y[n]=h[n]\star x[n]$
In your case that's the filtering with filter function. Now in order to get the impulse response you must convolve your signal with the inverse filter $f[n]$. Generally that's the time-inverted sweep signal (although special kind of pre-conditioning, amplitude scaling, etc. might be done as well):
$h[n]=y[n]\star f[n]$
Now you have your impulse response that you can use for further analysis. Please take a look at this answeranswer tackling very similar problem.
For more theory please see:
A. Farina - Advancements in Impulse Response Measurements by Sine Sweeps
A. Farina - Simultaneous Measurement of Impulse Response and Distortion with a Swept-Sine Technique