...she can reload a single barrel of a one-handed or two-handed firearm as a swift action once per round. If she has the Rapid Reload feat or is using an alchemical cartridge (or both), she can reload a single barrel of the weapon as a free action each round instead.
The second sentence states an exception to the rules of the preceding sentence, so "a swift action once per round" becomes "a free action once per round".
So assuming your shotgun is fully loaded before your turn, yes, you can full-attack, but you won't be getting more than a single extra attack that round, from one barrel.
Full-attack: -4/-4/(swift or free action reload)/-5
or +0/-5/(swift or free action reload)/-10
I'd suggest skipping on rapid-reload, since it otherwise has no relevance to advanced firearms.