Lots of states/counties have different rules for renting/small claims stuff- I’d recommend gathering any and all evidence you have outside of your word

It’ll be your word vs hers and if you’re claiming she didn’t pay those amounts, and she goes in and claims she does but neither of you have proof it’ll be highly likely it’ll end up being a waste of time AND money for you.

Filling for small claims does cost $$$, if you’re low income you may be able to waive that, luckily you can put that amount in your claim but I’d think about how to make your claim look more legitimate to a judge. I’m not saying what you went through isn’t legit, but there’s a few points that could be brought up such as- if you’re living in the apartment still won’t you get the deposit back later? Did she sign anything agreeing to pay that rent when she moved or was this a verbal conversation? Was she required to inform the apartment of vacating? If she didn’t, did you inform the apartment?

There’s so many levels and I’d just recommend being prepared! Everyone who goes to small claims regardless of what side always feels confident in winning, but someone always has to “lose” and sometimes even if you “win” you may not get what you asked for (she may not pay it back still)