Rental agreement - Notice period

I am a tenant and had rented an apartment with a 11 months agreement (started Aug 2019) mentioning 2 months notice period. I had informed my owner, a month prior to the termination of agreement that i would not want to continue and vacate at the termination of the agreed term.My understanding of notice period is that, it is applicable only if i am to vacate before the 11th month (July 2020).Please correct me if my understanding is wrong!I I am paying my rent until 11th month. The issue is that the owner is quarreling with me for not informing her in advance i.e, 2 months prior. She even tried telling me i am supposed to stay back until Aug 2020 which is breach of the agreed tenure. Also she is asking me to hand over the keys even before the termination of terms (July) so that she finds a new tenant to settle me with my security deposit.I am now at my own house within the same city due to lock down,it was for my work that i had to rent this apartment.I just wanted to confirm on the notice period requirement.