Cousin's (26f) daughter (8f) has charged over $300 to my (21f) debit card through cell phone game app.

Final Update: Thanks all for your help with this as well as with my cousin. I realize that she's suffering right now, but this isn't new behavior for her and I see how miserable our family members are having to deal with her regularly, so I wasn't about to allow her to do that to me.

I was able to use a neighbor's laptop to access my play store account. Google instantly refunded the charges and I am now waiting for them to "fall off" my account. I contacted my bank and they said that it's ok to pay my water bill tomorrow, despite having only $25 in the account, because any fees I incur will be credited back if the Google charges don't fall off in time.

My cousin came back to my apartment with police escort, saying she felt unsafe and wanted to make sure I didn't harm her child. The officer spoke with me after my cousin left and basically said I did nothing wrong and he had no reason to believe that I had harmed or would harm LC. So I'm happy with the outcome and I appreciate all the support and advice.

My cousin and her daughter came to stay with me a few days ago as my uncle (cousin's dad) is dying and is in a hospital in the town where I live and go to college. I agreed to watch my little cousin (the 8 year old- LC) in between classes so my cousin can visit her dad at the hospital. He's in ICU and LC is not allowed in.
Of course, I've got a lot a homework and because of this I gave LC my phone to play with since my cousin takes the phone LC normally plays on with her to the hospital. LC asked me on Tuesday of she could download an app. I made sure it was age appropriate and downloaded the app. What I didn't realize was that I didn't have parental controls on my purchases. I only use Google pay for my music, so I guess I never thought to input parental controls.
Anyway, I got home from class a few hours ago and I checked my email associated with my app store to check the due date for my music app. I had 3 emails from Google concerning my purchases. Each email then had several "mini" transactions, totaling nearly $300 in around 10 transactions. I freaked out and thought my debit card had been hacked. I checked my bank account online and sure enough there are numerous charges that correspond with the email purchases.
My cousin hadn't left for the hospital yet, so I told her that LC had charged nearly $300 on my debit card in app transactions. My cousin immediately asked LC if she had made the purchases and LC said she had no idea what we were taking about. I asked LC if she had bought gold in the game I let her play as she admitted that she did, but said that it "isn't real money". My cousin explained that it is "real money" and that LC needed to apologize. LC became very upset and apologized through her tears. I completely believe she didn't know what she was doing.
As my cousin was getting ready to leave, I asked her when she thought she would be able to give me the money LC spent, since my electricity bill and water bill are due next week and I no longer have enough money in my account to cover these bills. My cousin said she didn't feel responsible for the money LC spent since I gave LC the phone without having parental controls in place.
Is she right? Is this on me? Do I have any recourse here? I know my cousin isn't well off. She has 2 other kids and they are with their dads while my cousin and LC are with me. LC isn't able to stay with her dad because he's in jail and has no family within a thousand miles of here. So I feel like $300 is more than they could even afford. But I don't feel that it's fair to ask me to cover the expense when she knows I live off of a very limited budget (under $10,000 a year) and she works a full-time, $15 an hour job.
TL;DR: I let my cousin's daughter use my phone to play a game. She charged nearly $300 to my debit card and my cousin doesn't think she should have to pay for her daughter's actions. Is there anything I can do immediately so that I can afford my electric and water bills next week?

Update: I called the water company and the electric company. The water company told me I had until the 24th to pay or they're cutting my water off. The electric company said I could make a payment arrangement, but that it would probably lead to them placing another deposit on my account in the amount of $125. I have $825 a month to live on. My rent is $400. I have $25 in my bank account and won't have any more money into November 1st.
Update2: I contacted my cousin and this happened. I know I shouldn't have been so rude and kicked her out of my apartment, but if she is going to talk to me this way there's no reason I should allow her to stay.
I texted my cousin this:
"I know that $300 is a lot of money. That's nearly half of what I live off of every month. I've contact (water & electric companies). (Electric company) is going to charge me a $125 deposit if I make a payment arrangement. (Water company) is going to cut me off if not paid by the 24th. I have $25 in the bank."
Followed by:
"I'm currently trying to get the charges reversed. If I'm not able to I risk losing everything. I'm going to ask for more shifts at (job), though it's difficult with my schedule."
Her reply:
"My father is ****ing dying and you're worried about 300 bucks? You shouldn't have even let (LC) be on the phone in the first place since you're supposed to be watching her! We'll be leaving tomorrow morning when my dad's released."
To which I responded:
"First, I never agreed to watch (LC). You asked for a place to stay and I opened my home up to you. When you discovered that the hospital wouldn't allow (LC) in to ICU, you brought her back here and dropped her off. I missed class on Tuesday because of that. You just assumed I would watch her without considering my own responsibilities. You can leave tonight."
To which she responded:
"**** you! The only reason I'm even staying with you is because (her stepmother) won't let us stay at the house since dad's not there. I don't have anywhere to go tonight! **** you **** you **** you!"
And my last response before turning my phone off and going to do my homework:
"Get a hotel room. There's a Days Inn near the hospital that has rooms for $49.99 a night. If $300 isn't that much for you, you should have no problem paying $50."


Source.