You could actually change by rolling healer (my point is that experiencing other role overall will make you better player as you start understanding how mechanically it is played and what not.).
If you do want to try healing (if you say no, yet you never tried...what??) then I would suggeest going for something like rdudu becauseit has immense and diverse kit or mw monk wich is overall most user friendly healer class to play. Seriously, having healer alt makes your chances to play rated bgs in pvp guild atleast double.
Hunter/Warrior are easy to play hard to master classes, straightforward and exciting because action action action action and bladestorm/stampede when not enough action. Dks are similiar but it feels as if you rely on your enemy to be bad rather then there is much room to excel for yourself.
Rogue/feral only if you are not liked by anyone and your social image is dead as it can be already.
Palas look good, but mechanically I personally find them repulsive in accordance to what other classes offer.
Ele shams are really good in pvp, they feel like howitzer and panzer had a baby, you blast poor plebs to smithereens before theyr poor sticks and stones bounce off your bulwark, gg wp. Ench are rather one shot kind of playstyle, win or lose so people get bored of it quite fast.
Shadow priest is weird, never played it myself but it looks like skill demanding class - seen people be 0 with it and seen people carry teams in bgs with it also.
Hope my rant helps, cheers.