Aggro shorties are actually some of the easiest villains to take money from at 2nl, at least in my experience. Alright, to answer your questions; c-betting these guys when you miss is generally bad because of their tendency to push, especially c-betting this flop, in all honesty by c-betting this flop you have turned your hand into a complete bluff. What is the absolute best you can hope for on the turn and river? T, Q, even then you are still behind a flush. By c-betting here we lose any value we may get on a river A or K, all we are hoping for is to fold out the other guy, if this is our intent, why are we waiting for AK type hands to do it? 2nd reason not to c-bet, you don't even know what you are doing when you are raised. You should know the answer to what you are going to do in the event the villain calls or raises, your ranges should be formed based on these possibilities even before you bet, this stops us from making stupid decisions because omg, he raised me. Whether or not to call his shove; simple answer really, you bluffed, you got caught, now fold. Sure you have AcKc, a great hand pre-flop, but a not a great hand on that flop, you bluffed.
How to deal with them in general, if you have position on them, I add TT, JJ and AQo, AQs to my 3-bet range and am not afraid to stack off against them with those hands, they are generally stacking off with 77+ ATo+, fold anything smaller than TT to their pfr's cause you don't have set odds. If they have position on you, go to a different table.