It works both ways. Both the tenant and the property owner have laws and regulations they are required to follow. The property owner must not violate the tenant's privacy and barring a very real emergency, like a flood or a fire, cannot enter the tenant's home without giving notice, in most communities it is at least 24 hours notice, and more in some places. The property owner can have access to the property if it is for a valid reason (not snooping or harassing) and if he or she provides the legal notice required.
If you have a receipt for the rent you've paid, it doesn't matter whether you have a lease. You still paid your rent for so many months and you have proof. You can take your landlord to small claims court, which costs little and no lawyers are allowed. It wouldn't hurt to see a lawyer for an hour or so to learn what your rights were, if they were violated, and what your choices are, and to get your evidence and argument in order should you choose to go to small claims court.
If you don't have a receipt, or a copy of a check you gave her, or anything in paper to prove you paid rent in advance, then I think you are out of luck. Never, ever pay anyone anything without obtaining a receipt! If need be, carry your own receipt pad you can pick up at any store selling office supplies and write out your own receipt and request their signature on it before you hand over the money. I gave one to my child after one too many landlords played rip-off games and conveniently never could seem to provide a receipt. It is way too common for property owners and property managers to take advantage of young people.
The property owner does not have the right to check up on you all of the time to ensure you are doing things exactly as she or he wants. When a tenant pays rent, he or she is paying for that property to his or her Home for the duration the rent monies cover. Also, a tenant is not responsible for normal wear and tear of the property. That is the cost of doing business for the property owners. Sure, a lot of property owners take advantage of young people and low-income people without the knowledge and/or resources to stand up to them and fight back, but that doesn't mean it is actually legal. So when you rent, write down Everything you can find wrong with the place, date it, sign it, make a copy of the dated and signed document, and turn it in. Then when you leave, do the walk-through the owner is required by law to do with you, compare the place to your original document, note that you are not responsible for repainting, cleaning carpets, refinishing wood floors, because that is all normal wear and tear. You are responsible for things like breaking light fixtures, ripping up curtains, punching big holes in the walls, but Not normal wear and tear of daily life. After the two of you have agreed what you are or not responsible for, make the owner sign a final document settling things so he or she cannot come after you unexpectedly later with bogus charges (which is a notorious scam commonly pulled by property managers and owners). Protect yourself, otherwise, you will eventually end up paying for what you don't owe and being ripped off, at least once.
I don't think it was legal for you to change the locks. Next time, if a landlord is violating your privacy and the law, send him or her a registered letter politely and respectfully stating the problem and that you are asking him or her to follow the law from that point forward. Be sure it has to be signed for upon receipt so you have proof you sent it, and be sure you kept a copy of the signed letter. That way you have proof you tried to work it out, that the owner was violating the law, and it is illegal in many places to punitively evict a tenant for exercising their rights.
Also, you can look into whether your city/county has a tenants advocacy office or group, and also find out with what state or county agency you can file a complaint against the property owner.
Good luck, and I'm sorry you were taken advantage of by a whack-a-loon. There are a lot of them out there.