Part 1: Do physical states cause mental states?
What you are describing is commonly referred to as a mechanistic view, most famously advocated for by Descartes. While he claimed that this view can explain what appears to be mental states in non-human animals, he did not think if it could account for human mental states:
Although his conception of animals treated them as reflex-driven machines, with no intellectual capacities, it is important to recognize that he took mechanistic explanation to be perfectly adequate for explaining sensation and perception — aspects of animal behavior that are nowadays often associated with consciousness. He drew the line only at rational thought and understanding.
He believed the mechanistic view could not explain two aspects of human intelligence:
The mechanistic explanation of behavior does not apply to human
beings, according to Descartes, for two reasons. First, human beings
are capable of complex and novel behavior... Second, human beings are
capable of the kind of speech that expresses thoughts.
Most modern philosophers who defend the mechanistic view (such as Peter Harrison and Peter Carruthers) do so by saying that arguments for animal consciousness are flawed. This type of argument is not very strong since it can be (over-)simplified as 'Because no one has proved me wrong, I must be right'.
If we accept the hypothesis you describe, that the mental state of a human is merely the results of the physical state the human is in, we would have to both advocate for a more extreme mechanistic view than Descartes proposed and explain how a physical state can give rise to a mental state. I want to stress that a person can hold this position, but they would have an extremely hard time defending it.
If you wanted to defend it, I would suggest looking into the field of mental causation (described here and here). It is primarily concerned with how mental states can result in physical behavior, but it is a place to start if you want to do more research.
P.S. Even if mental states are completely deterministic, that does not imply that free will does not exist.