Should the measurement uncertainty be included in the random uncertainty?
Yes - to calculate the total uncertainty when adding or subtracting measurements, it's the room-sum-squared of all the uncertainties. 

$$
e_{tot} = \sqrt{(e_{meas})^2 + (e_{rand})^2}
$$
The more generalized form of this will be the root-sum-squared of all sources of error and uncertainty.
$$
e_{tot} = \sqrt{\sum{(e_n)^2}}  
$$

To get the quantity "$e_{meas}$" you apply the root-sum-squared formula of all the uncertainties of your measurement devices used to transfer liquids (transfer beaker, graduated cylinder, burette, etc...). 

$$
e_{meas} = \sqrt{(e_{beaker})^2 + (e_{burette})^2+(e_{grad.cyl})^2+(e_{burette})^2...etc}
$$

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To answer whether you apply the burette uncertainty to your measurement, the answer is also yes. Assuming that the burette has an uncertainty of $±0.01 cm^3$, the actual reading of your measurements will be: $33.3cm^3 ± 0.01 mL$ and $33.4cm^3 ± 0.01 mL$. The two uncertainties in the measurement will be applied to the $e_{tot}$ equation above.