Can I make health decisions for my father when his sister is power of attorney?

Greene, by using "POA", are you referring to a DPOA, or some type of Medical authorization, such as a Living Will?   The former typically addresses financial and similar type issues while the latter addresses medical type decisions.

No, he can, however, give you permission to talk to the doctor. I would TT him about changing his durable POA.

The technical short and legal answer is NO if they have medical PoA, but read other comment below regarding cirumstances.

Health decisions get made all the time without the carer or anyone else having a POA. The only problem comes if there is a disagreement – with the carer and the LO if they are still able to make decisions, or with the carer and someone with a POA if you don't agree. The best option is to talk to Sister and reach a broad agreement about who does what. If Sister is being a nuisance over small items (or just throwing her weight around), and you can’t smooth it out, talk to Father about perhaps changing the POA to you as carer. If there is a major disagreement (like Sister wants you to care for Father at home and you think a facility is better), come back and tell us more about the details.