Retaliatory Eviction Rights As a tenant

I rented space with a woman and her daughter for me and my daughter. The space was 2 bedrooms in her home, sharing the common living spaces. She crafted a lease but neither of us sat down and signed it before I moved in. After 2 weeks, she decided our living arrangements wasn't working. She claimed I damaged her property (a cracked stovetop), didn't fully clean the kitchen to her satisfaction and clogged the toilet. I had already paid her the entire month's rent but she asked me to vacate 10 days into the month so I asked for the prorated amount in return.
She first told me once I moved in I assumed the lease was valid even though neither of us signed it and I must adhere to the terms of that lease. Now she says I was considered a lodger not a tenant since she lived on property and I don't have the typical rights as a tenant. She is keeping the entire amount I paid plus she says I owe her more due to the repairs needed.
I need to know what rights I have. I believe she is using me to pay for an already damaged appliance the she has now replaced (vs repaired). I am on a super huge budget, don't have any extra money but if I need to go the legal route to get my money back from her, I'll find it.
It seems under the scenario you describe that you are a tenant.

You may find some help here:

If you have a copy of the lease agreement, even if unsigned, it can serve to show the intent was tenancy. However, without the signed lease agreement your protections are the same as a month to month tenant as defined in state statutes.

It seems you are not required to move out yet and have not been given proper notice. Have you been given anything in writing defending you leave? Have you actually moved out yet?
I need to know what rights I have.

If you disagree with someone over something, you must take the matter to court in an effort to resolve it.

There are no magic words, mystical dance, or spell you can cast that will make another person do your will.

The same can be said for the other party.

However, the other party possesses your loot.

The only way for you to get any of that loot back is go to court, tell it to the judge, pray the judge rules in your favor.

The sad part of this story is that if the judge awards you $3,000, the only way to get that $3,000 is to collect it.

That means you can have the sheriff seize it from her bank account, attach her wages, etc...

Successfully suing someone is easier than collecting a judgment against someone.

All across the USA fewer than 1-5% of all judgments are ever collected.

The good news is that the landlord can't kick you out.

She can ask you to leave, but you can stay.

She will then be forced to go to court and have you evicted.

You, on the other hand, don't want her to file an eviction.

If she files an eviction, you'll have trouble renting decent "digs" for decades, if not the rest of your natural life.

An eviction will probably destroy your FICO.

I suggest you find yourself new digs ASAP.

That means get busy getting, before this turns nasty.

Going to court isn't fast, and is most often unsatisfying.

Good luck.
I do have the lease, it was sent to me electronically. In fact, all communication we've ever had regarding to conditions of the home and her asking me to leave have been via text or email. So at least there is a record of that.
She asked me to leave by a formal eviction letter and I did so by that date. She only gave me a week's notice but that was what I call "hell week" because of the passive aggressive treatment from her and her daughter.
It seems the only way to recoup my money from her is by going to court but that process probably requires funds I don't have.
Since you are already moved out then your resolution to this is with the court if you are not able to come to terms with the landlord.
I suspect you could likely get a judgment in your favor fairly easily.
If you are low income you might qualify for a fee waiver and be able to go to small claims at no cost.
Be aware that court is not a quick process, nor is collecting if you win.