As the poster above said you have a separate pvp profile under the 'character' sub menu. If you haven't seen any level gains yet you probably haven't won many matches, as you get more xp for wins than losses.

You also wont get any pvp abilities till at least lvl 4 if I remember correctly.

Remember to get your challenge log unlocked as theres 400 pvp xp a week just sitting there for free, 200 for running 10 matches and another 200 for winning 3.

Happy hunting!