Travel Expense - Year Contract On Location In Another State

I am a contract worker through an employment agency (not a 1099 employee).  My permanent address is with my parents in my home state where I will also pay taxes, but I had to rent an apartment in the contract state in order to complete the assignment as I could not work remotely. The contract was for a year, but could terminate in less than the full term at their option. 

 

Can I deduct travel, rental housing or other expenses associated with my assignment location as well as monthly travel back and forth between the two states?  Similarly, since my doctors and dentists are still in my home state, can I deduct mileage to and from my doctors from my contract state to my home state as medical mileage?

 

My car, voters registration and drivers license are all still showing residence in my home state.