Is my cat depressed?

My cat is called Suzy and she is 16. She usually stays in the kitchen where her bed is but today she was hiding under my mums bed and just wouldnt move at all. She had a sort of sad / nasty look on her face and yet when I tried stroking her, she did not purr which she always does. I could not tempt her out with food either. I had to push her out but she didnt move her paws at all. Shes been a bit sick lately too, does that have some effect on it? Also, [it may have just been me] but she doesnt walk as steady as she used to and isnt as perky. Is it a wise choice to take her to a vetranarian or is there a simple solution?