You've gotten some good advice, and some not so good.
You can get a cheap gun "locker" from wal-mart for under $100. Not so good for determined thieves, but will keep guns secure from unauthorized people from laying hands on them. Not ideal, but simple and effective for this type of use. You mention (or imply) that she HAS to have access to the guns for defense,....well, no she doesn't, particularly when she is drinkning. IF an intrusion happened when she was under the influence, oh well. The risk of having guns accesible to someone that was not stable when they were drinking is higher. Too bad. Playing has risks, and no guns available may have to be one of them.
I've been on the drinking girlfriend road before. Think about a couple of things. From your description, she is NOT stable when she drinks. Happy-mad-happy-mad-happy........Even tho there was an argument with girlfriends, the "reason" doesn't matter, it's the result in that situation that does. She could very well be mad at you some time, and start a fight, (argument). Guess what, IF someone, neighbors etc, called the cops because of the noise, and they show up to a domestic argument, and you have guns in the house,....well, in many places you are assumed to be dangerous in that situation, and your guns may be taken, even if temporarily, no matter who started it or why it's happening. If it got worse, like she slapped you and you pushed her into a chair to get her away from you, it can get real stinky. She only has to say you did such and such, (whether true or not, it's not provable either way) and your guns are gone. Sometimes you can get them back and sometimes you don't, ever. And you can't go buy any more. Ever.
Frequency of heavy drinking has NOTHING to do with whether someone is an alcoholic. It's not that simple. It has to do with how they drink, how much they drink, how they act, and why they do it. Once a week, once a month, even once a year, is not an indication of an alcoholic or not. From personal experience, and what little you told us, I think she's an alcoholic. It doesn't even matter if she is or isn't tho, what matters is how she acts when she's drinking to excess. She may have other problems as well, we all do, but this one is a problem that is not likely to go away by itself.
Go get a cheap gun locker. No mattrer what esle you do, and DON'T give her a key. You can leave it open, or some (or all) guns out when you want, but have the option to lock them up.
I ended up getting rid of the girlfriend. It finally took a stalking protection order.