Yeah. It's totally okay. Don't feel embarrassed. If she comforted you that means she cares and if she cares then it's okay to be yourself around her. Don't hide your emotions. I'm so sorry for your loss by the way.
I am sorry for you loss. Don't worry about it at all. You just lost your mother, when else would you break down if not in such a situation? Hell, bawl as many times as you need to. If your gf's weirded out then she needs to deal with it, not you.