I got my flu shot this year, but I've gotten sick and my symptoms include muscle aches and fever. Is it possible I have the flu?

Yes. Yes, it is possible. Ultimately the purpose for the flu shot is not to prevent the flu, rather it is to prevent you from dying from the flu or flu related illnesses. That said, the flu shot does reduce risk of getting the flu and often makes the bout less severe if you do get it.
Yes . The flu shot decreases your chances of complications from influenza, like pneumonia. A flu shot will not keep you from getting it.
Yes. The flu shot has activity against the predicted most likely flu types thought to be present for the year in which the shot is given. But you can get other types or a mild form of the common type. Unless you are very sick, you can probably take off from work, rest, and take the usual anti-cold therapies over the counter.