Can you sue if you are not paid the money you are owed?

Firstly, there's no contract whatsoever so my initial thought is that i'm screwed. Basically, my phone got stolen and the person who bought it contacted me because she couldn't use it because the phone company told her it was stolen and inactive. So she was going to give me back the phone OR I would sell it to her for a low price of $250 (iphone 5). She went on vacation and to be safe I made her pay $100 as a deposit and she would pay the rest when she got back. When she got back I messaged her because she made no efforts in messaging me and she told me she promised she would pay me the rest when she had the money, HOWEVER THE PHONE GOT STOLEN IN MEXICO ON VACATION, so my assumption is that she does not want to pay the rest. The only proof I have are text messages talking about the payments she would give me. Can I file a lawsuit or no? I just feel so wronged, she keeps ignoring me now.

You can always sue, but proving that you had any claim at all is almost impossible. Why on earth did you make a deal to sell you own phone to the person in possession of stolen property? That sounds very sketchy, and you'll have fun convincing a judge of anything.

"Firstly, there's no contract whatsoever so my initial thought is that i'm screwed"

And your initial thought is correct.

If she paid the $100 dollars to you, you have no legal recourse since the phone is no longer stolen, she just isn't living up to a contract. So you can try suing her for $150 dollars, but how are you going to get a summons to her when you don't even know who it is? Plus, even if you sue her and even if you did win, you have no way to make her collect.

I would just take this as a $150 lesson in not trying to negotiate with thieves and to keep your phone in a secure place on vacation.