What to do about my dog's barking?

My dog is a chihuahua/beagle and she has horrible seperation anxiety. She whines and barks. I’ve already gotten in trouble at an apartment complex because neighbors complained about her barking. I just moved to a new apartment complex and I don’t want to get on the wrong foot. I’ve been using a muzzle for when I leave for work, I take it off of her when I get home but she looks like the muzzle irritates her. Also even with teh muzzle on her she still is able to bark pretty loudly, the apartment walls are very thin.

What should I do? I want something that will be effective and not hurt her.