Invite girlfriend to prom?

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Hey guys, I (19) have a complex situation and I would be thankful for any helpful advice.

Well, first of all, I have a girlfriend (22) and a best female friend (19) who, even if she is really close to me, doesn't know that I have a girlfriend. It really isn't that I wanted to keep my best friend on the hook, becoming a girlfriend just isn't a thing I wanted to burst out as some other guys do, since I don't think that it's something THAT special to tell the people.

However, it happens that my prom will be next week and I'm going to dance with my best friend which my girlfriend knows about.
I would probably spend the night with my friends and the best female friend (which are two different groups), so I don't know whether I should also invite my girlfriend who knows nobody.

My problem is that my best friend might be disappointed that I haven't told her anything about my girlfriend and she is also going to make her hairs curly because of my request.
Besides, it might be uncomfortable and I wouldn't be able to spend the last time to probably see all my friends together as I would do without my girlfriend.

Thanks in regards.