You probably need to fix your Pokémons' movesets, because right now they kind of suck. For instance there's absolutely no reason to keep Confusion around when Psybeam is a straight upgrade to that. Is your Meowstic male or female? If it's female teach it Charge Beam and change its ability to Competitive if you can; if it's male teach it Light Screen and Reflect and change its aility to Prankster. Next, your Pansear has three Fire attacks, switch the weakest one out for something else, unless you absolutely need it to set the Field on fire. You'll want at most two attacks of the same time in your movesets and even then only if they serve different purposes.
Pidgeotto and talonflame are still using the most basic moves of their types - Quick Attack is fine, but stuff like Gust or Ember isn't gonna cut it at this point. Switch them out if you can't give them any better moves right now. Your Swampert should have learned Rock Slide some time around Corey, did you keep that? Swampert is a great tank and its only weakness is Grass which Shelly has only covered with Masquerain and Yanmega.
In case you din't know: a "timid" nature means that the Pokémon has a reduced Attack stat and you've got that one two physical attackers. In the future you should look out that your Pokémon at least don't have Natures that reduce their key stats.
Anorith is very slow when it's not raining, so if you focus it the turn it comes out your birds should be save from it.
Araquanid is very slow as well, so focus it once it shows up, especially if you want to rely on the burning Field. A big part of its power comes from its ability which reduces the damage from Fire attacks and doubles the power of its Water attacks; Gastro Acid, Skill Swap and the like can be used to get rid of that ability or you could focus it with your strongest Rock and Flying attacks.
I'm convinced the fight should be doable if you change your movesets and rethink your strategy based on those new movesets, but if you want to or think you have to train some new Pokémon here are my recommendations:
Growlithe is available from the Beryl Ward police office once you found all the missing officers. It comes with a random Egg Move, I recommend Close Combat for an offensive set or Morning Sun for a bulky set.
Numel shows up at the Peridot train station under rainy weather. It learns a number of good moves, including Rock Slide, fairly early and Camerupt's Hidden ability reduces the damage taken from super effective attacks. It's only really worth it if make sure you get that Ability though, since it's so slow that it absolutely will eat attacks before it gets to do something.
Onix is a gift from a hiker in Peridot Ward, if you help him find a house. It's quite fast for a Rock type and learns Rock Slide; it also has some utility with Sturdy, Stealth Rock and Rock tomb.
Lastly, make sure to search everyhwere for hidden items. Suspicious rocks, corners and the like will often yield usefull items like Gems and Seeds, as well as Shards to trade in with the move tutors later on.