First off, in the internal energy equation, q is heat gained by the system (if you refer to the variable without a negative sign). Work is always done by a system when there is a change in volume. Thus for a reaction which occurs at constant pressure and involves a change in volume, there is indeed work done by the system. However, enthalpy is by definition a measure of the total heat content of a system, and the change in enthalpy is thus the change in this heat content. Because you operate at constant pressure, no heat is acquired/lost through work, and thus work done does not affect the enthalpy change. As a counterexample you could imagine gas changing temperature as it does work to expand.
Keep in mind that the concept of enthalpy was designed to be a useful measurement mainly for isobaric conditions (sometimes you will see isochoric problems allude to it). Under other conditions, internal energy is usually utilized. The equation ΔH=ΔU+PΔV is an intermediate in the derivation of enthalpy; you will almost always encounter your enthalpy change in terms of heat transfer q. The +PΔV term is added for the purpose of being able to state a mechanically sound relation to internal energy, ΔU, and thus define enthalpy universally.