Silverthorn, i'll try to give you some support. as i am not a native english speaker please be tolerant
At first you have to compare patch 5.3 with the beginning of a new pvp season but without the differentiation of mmr.
so you battle against experienced pet battle pvp player. without practise, you have to be patient.
so here are some points where you eventually could improve your win/loss ratio. DON'T choose pets because of their style or "because it is so cute". make sure that in the beginning of the fight you recognize the basic strategy of your opponent. like in "real" pvp, you enter the arena and by sight of the opposing team you think what might be best and what will the opponent do. key to that is knowing the enemy. you see his 3 pets and by that you should know how he wants to defeat you ... what is his plan. you REALLY have to know strong/weak attack/defence to counter his pets.
in the beginning you have to consider your comp, 1) dot line up 2) heal dominated 3) burst 4) cc/debuff dominated, there might be more or rather subclasses like weather dependent but these are some important categories. so you have to choose your pets accordingly.
to start i would concentrate on either burst or rng cc as i'm successfull in it and i prefer shorter fights. heal dominated teams are frustrating as long fights are annoying. rng cc is mostly miss chance or ability with an percentage to stun due to sandstorm, darkness or debuffs like stench. lets say you start with sandstorm, apply stench and your opponent wants to use an ability with 80% hitchance. so he has 50% hit chance left, here dot teams with chains like goo-corrosion-absorb or pets with ramp up are screwed.
so you have to generate synergy effects between your pets. don't choose "stand-alone" pets, they might be good in itself but against a team with a functioning synergy you will be defeated.
eg a pet with call lightning and a second fast one with a multiple attack, like a serpent for lightning and a rabbit
or minefield + grip of crawling claw or magic broom
or bleed + a pet with an ability that benefits from bleeding (a bleed has the advantage that you are not dependent on weather effects) eg electrified razortooth + curious wolvar pub (the trap is REALLY a pain)
or very fashioned is snowman + kun lai runt due to obvious reasons
obviously there are many ways, these are just examples
beside that you have to choose a "third" pet, a good pet that comes last in most of your fights, like blighthawk or stitched pup or any mechanical (strong heal + ud racial) even if you have to react to your opponent, you should have some kind of order. in my team all three pets benefit form each other and if i have to adjust it is no big deal.
nowadays in most teams there is at least one kun lai runt, anub idol or monk, so you should have an undead or a maggot/snail/ooze with absorb or a strategy to counter klr and you should consider a pet with weather effect to counter sandstorm. in your armory/pet collection there are some really good combinations possible without further farming/investing in the auction house. Think around the corner
So if you need further help or direct support post your team. Good luck!