How do I fix a t-shirt that is WAY too big?

I am starting to volunteer at a hospital and we are required to wear their uniform t-shirt. They only carried larges (not even a medium was available). I am a very petite person who wears an XS. I had to buy it no matter what because I'm starting soon and they don't know when the mediums will be in stock. They said the company who manufactures the shirts don't make small sizes at all.

The t-shirt is:

- way too long (easily fixed I guess)

- way too wide

and the shoulders are way too wide! The sleeves seem like they would be an ok length if ONLY the shoulders weren't so wide.

Do I have to go to a tailor to especially fix these issues? I obviously can't make it "look cute" or "fashionable" since it's a uniform. Is it even possible to fix the shoulders?

How much might it cost if I get this done at a tailor? I live in Southern California so it must be more expensive. T___T