Yeah, no. There's a bunch of problems with that list, unfortunately.
-You have nowhere near enough draw power; getting stuck with a bad hand early-game will kill you unless you've got a lot more than that (standard is 3-4 Sycamore and 2-4 Birch/Shauna, plus a Shaymin-EX or two if you've got that).
-Electrike AT isn't actually the best choice of attacker, since it relies on a different type of Energy than Beedrill does and consistency is already a problem for this deck. Since you already have access to plenty of Switches and Float Stones, I'd recommend Miltank, since it's got a [C] attack and can OHKO Vespiquen and 2HKO Seismitoad-EX if it's got a Muscle Band attached and Beedrill on the Bench. (This is very important, because Vespiquen decks are so fast that you can't keep up the Prize trade if you're relying on elaborate 2HKOs like this deck does and Toad shuts down your Switches). Celebi XY93 might also work; I'm gonna ask if its Sparkle Motion (which places 1 damage counter on all opposing Pokemon) counts as "damage by an attack" for the purpose of triggering Allergic Shock. If it does, it's worth using those, since a KO on it only has a 50% chance of actually being a KO due to its Ability. Either way, you should also drop Yanma/Yanmega, since the attack you're looking at there to go along with the free Retreat is extremely expensive.
-There's a lot of decks out there focusing on mons that have either a low retreat cost or none at all, and that ruins Allergic Shock's strategy. As such, you're going to want a way of keeping them trapped there. A 2-2 line each of Ariados AOR and Dragalge FLF will stop all of your opponents' non-Grass mons from retreating manually. Opposing Zoroark can slow this strategy down a little, but most decks don't run multiple Zoroark, so you should be able to get rid of them with relatively minor delays.
-Herbal Energy is basically useless, since solid attackers are fairly likely to OHKO Beedrill anyway. Switch that to basic [G], and change the Flash Energy cards to the same thing, since Electrike is no longer your attacker. This allows you a little more flexibility with Professor's Letter.
-Your mons are going to be dying relatively often in a deck like this, so a couple of Super Rod cards will allow you to last much longer. A copy or two of Teammates will also be useful, for the same reasons.
-Poke Ball isn't really worth it due to its unreliability; I'd convert that to another Level Ball or some other useful Trainer.
-Unfortunately, due to deck space constraints, you'll need to decrease the count of Skyla, Judge, and AZ (unfortunately, you don't have enough Energy in the deck to make AZ-based switching viable as more than a one-off tactic), and you'll probably need to drop Xerosic entirely. In a similar vein, you either want a 4-2-4 Beedrill line with the Rare Candies or 4-4-4 without them (either one works due to your Stadium); you just don't have enough available space for both with all the cards that have to be added to make this deck viable.
I don't have time to try and construct a full decklist now (I'm on a quick break from working on a major project for my lab), but I'll be back at some point in the next couple of days to help you improve this, because Beedrill is absolutely hilarious if you pull it off right.
EDIT: Celebi's Sparkle Motion does NOT count as doing damage to trigger Allergic Shock, apparently, so stick to Miltank as the primary attacker. I'll be back in a bit.
), but things that would allow us to search for Beedrill Partners a lot easier.
