I think you are probably missing a piece of information to do the conversion. Your signal in MATLAB is probably in some arbitrary digital unit, you need to know the conversion from MATLAB units to voltage units. With that and teh microphone sensitivity, you can convert your signal from arbitrary units to Pa.
You then need to A-weight the signal. The A-weighting filter coefficients depend on the sample rate. You also need to account for any non-flat frequency responses in your microphone, preamp, amp, and analog-to-digital converter.
Once you have the A-weighted signal in Pa, I like to convert the signal to intensity (W/m2), which you get by squaring the signal in Pa. The instantaneous level in dB(A) is then 10*log10 of the signal in W/m2. The mean level in dB(A) is the 10*log10 of the mean of the signal in W/m2. Often people want the peak level based on either a "fast" or "slow" integration time. The integration times are standards and you will need to implement the weighting window...
The easiest way to do all of this is probably to use something on the FEX. The following looks promising, but I have not tried it: