One on one, I can take down most warriors with relative easy by dotting, kiting and keeping shield up along with well timed Fear + trinket out of hamstring. Of course, you wouldn't have this luxury in arena and have to deal with said warrior receiving heals. So this leads to one of two strategies.
1) Your teammate CC's the healer while you test your luck alone with the warrior. If you feel you don't have the gear, resilience and faith in yourself to do this, then try...
2) Your teammate obstructs the warrior so you can get away from him. At this point, you should keep dots on the warrior while fearing and mana burning the healer. When the warrior turns red that is your cue to SAVE that fear (he'll be Immune) and head for a pillar/around a tomb/ you name it.
Be sure to utilize Focus Targeting here. I use the Proximo addon for arenas and you can click on their unitframe and set focus easily that way. Set a macro to Silence the Focus Target and Target Focus the healer. I have something like this:
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/cast [button:2,target=focus] Silence; [harm] Silence
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This makes Right-Click Silence the Focus Target so you don't have to manually switch to the healer, allowing you to continue nuking the Focus Fire.
When the warrior/dps class is down to around 30-40%, time a 5-point Kidney shot with your rogue friend and right click that silence macro and start nuking HARD on the Focus Fire. Follow up with a fear if you have to. If it's a paladin healer, be sure to dispel Blessing of Freedom, otherwise the warrior will have no troubles catching up to you, and LOS as much as possible, never stand out in the open since you don't have a true healer, and also to avoid charges and intercepts.
As far as gear goes... Get the "good" honor trinket first if you haven't already. From there, work your butt off getting that resilience up. 10k HP unbuffed and 300+ resilience starts to make you a lot harder to burst down. I chose a
[Resolute Cape] with 120 Armor to Cloak over the honor one because I feel I'm more of a tank and most fights depend on how long I can survive or IF I can survive.
The hardest fights you will have would be 3v3/5v5 when you have a rogue+warrior on you with poisons and hamstrings. You have to rely on solid CC'ing in those cases. I hope I've helped you out some. Good luck.