The pre-80 bracket is extremely unbalanced, so I wouldn’t worry about that. You’re playing against people who are using partial set bonuses from the last expansion and may have stacked versatility over pve stats.
You will probably be level 80 by the time you read this so much of your concerns may be resolved when you get your pvp honor gear.
In that regard, your current baseline item level is a huge problem, and it actually may be 60% of the issue here.
As soon as you hit lvl 80 get your starting PvP gear from the honor vendor in Dornogal, it will raise your item lvl to 626 in PvP and will also give you a huge versatility buff.
I play 2v2 most of the time, and in that setting there are some matchups that are near unbeatable.
I would say don’t worry about losing streaks for now, just find a friend and farm your weekly conquest points.
All that being said, as frost spec, you should be coming out on top over warrior most of the time in 1v1 situations. In PvP 97% of the mages I have encountered in arena and bgs are frost speced.
I know that you are in that unfortunate squishy spot right now, but I think you should stick with it. Mage is one of the most rewarding classes in WoW. It has it’s ups and downs, but I think the holy trinity plus hunter (Warrior, Mage, Priest + Hunter) will always win out over the Flavor of the Month classes.
Just remember, you chose mage because it’s a very fun class and WoW Arena PvP is a footnote of a footnote of WoW content.
If you want to flex to other classes, remember that the Warband system encourages you to branch of each expansion and try new things out. There’s no harm in seeing if the grass is greener as a melee or healing class/spec. Why not give evoker a try? It’s essentially a mage with mobility on steroids.