So, Is there any way I could log in with my Hi Rez account name and password instead of the Aeria? I'm asking this just because I want to play with my friend who downloaded the game on Aeria Games, but I can't use my old account.

Unfortunately, no, not at the moment anyways. Aeria's version would be to be uninstalled and the C:\Program Data\Hi-Rez Studios folder deleted, then HR's version installed.