Your girlfriend’s idea of love is different than yours. You can’t call the police and fine her or ticket her for not loving you properly because there’s no code or laws to break in love. So you have to decide if this is someone who’s compatible in their love for you.
You already know deep down that the reason your girlfriend doesn’t tell you about meeting her ex or going off to a beach party for a week is because she doesn’t want you to be part of it. Her idea of having a boyfriend — or having you as her boyfriend — just doesn’t include being invited to the party. And it doesn’t include telling you the truth.
Since you’ve only been dating a few months, you’ve done your job and figured out what isn’t working for you. I’d say respect yourself and move on. You’ll feel a lot more comfortable with a girlfriend who doesn’t lie to you.