It isn't clear from what you have said whether it is you or your girlfriend who effectively contracted with the hotel for use of the room. The person who contracted for the room is the person who likely has a basis for taking legal action against the hotel for excluding you. Although you may have booked the room using your credit card, depending on what other information was provided at the time will decide whether or not you, your girlfriend or both were effectively parties to the contract. So in essence I think you need to work out who actually reserved the room and that person may complain about he hotel's refusal to allow entry.
Whether such a complain would succeed in recovering compensation will likely depend on whether a tribunal or court determines your having been excluded was reasonable in the circumstances. That will depend in large part on who the court believes when comparing your evidence and their evidence as to your behaviour and what they new about your role in booking the room. If the court accepts your behaviour was so poor as to justify their refusing to assist you or allow entry to the room, then likely you would be unsuccessful. witness evidence on this may be also supplemented with CCTV footage from security cameras which are common in hotels. Also relevant will be whether it was reasonable for the hotel to withhold access based on what information they had about the booking and the apparent fact that your girlfriend had made no arrangements for you to be admitted late at night, which would normally have been expected.
If you do wish to proceed with a claim then the place to bring it will likely be in your state's consumer claim tribunal (each state has its own system, but most have a tribunal, rather than a court to handle such claims).
I trust the above assists.
If you advise which state the hotel is in and which state you made your booking I can advise more specifically where you should bring such a claim if you wish to pursue action against the hotel.
Good luck and please rate my answer.