I think that you answered your own question young lady. You have to take care of yourself and support yourself. If you used all of your savings to come over here, I would think that you would have a great time with your friend.
However, If you spend all of your savings on something that will come to an end, and leave with nothing more than some pics and memories, and then you have no money to survive on, would that be the right thing to do?
I think you have to put your foot down here. You need to make sure you have enough saved for the rest of your year!
Can you visit her where she lives and not the other places? Trust me, LA isn't anything worth visiting.
I think that's the right way to balance it. you can minimize costs and still visit somewhere cool! where you coming from? welcome!