Sounds like you are on 'holdover' ie bound by the same conditions of the lease other than you are able to give the appropriate notice to vacate the premises.
You don't mention which state you are located, so it's anyone's guess the appropriate notice required.
As the lease was only 12 months, there is no question that the lessor was able to issue the appropriate notice to increase the rent.
Can you leave - yes, under what terms - the terms which relate to holding over.