I paid rent for 3 months at my last residence and where I'm currently living I don't pay rent (disabled parents residence) can I still claim head of house hold.

I assume you are NOT married.

To claim head of houseold, you must pay MORE than have the costs of maintaining a household for a qualified person. It seems doubtful that you have paid more than half of cost f maintaining a hosehold, but, assuming you did...

WHO is your qualifying person?