Has she got a load of new friends that you have never heard of before or just one friend who she has not mentioned to you? When you query her she will say that she has told you about her, so then it starts putting doubts in your head and then you start to imagine it is you with the problem.
She starts to argue with you for no reason, and then storms out, accusing you of always starting arguments. Has she taken a bit more care of herself when going out, for example: Spending more time doing her hair, wearing best clothes when she is out with the girls, showing a bit more cleavage or a bit more leg?
Never let a girl who you are in a relationship with go to a nightclub without you, there is a reason she does not want you there. Lads are bad when they are out, but believe me girls are twenty times worse.
It is very easy for girls to get noticed and even if they are not the prettiest there is always some lad in any town who will want to brag about going with that girl in the club last night. Check her mobile call history for numbers that have no names. Maybe even ring the number, and you never know it might be answered by someone saying hello sweetheart/gorgeous etc.
Only someone who is very close to your girlfriend would do this and it would certainly have their name next to the number. If she insists on going out with her girlfriends tell her you will meet her somewhere later on. See if she then has a change of plan, or texts(likely) or phones(unlikely) to say they have all gone somewhere else as it was quiet.
When you see her next time she will say she had no signal to let you know they had a late change of plans. Do not tell your mates you think she is cheating as it could be them who she is cheating with. It is very easy to catch a cheat, but you will know if she is cheating because your instincts and your heart will tell you.