Did I accidently sync my iPhone with a work computer? What have I shared?

Approving a "Trust this computer" request enables basic communication between the phone and a computer, it doesn't transfer data per se. Basically it ensures that others can't just take your phone, connect it to their computer and transfer all your data without you knowing.

With Windows you will probably see your phone somewhere in Explorer afterwards, mainly the photos should be accessible. But you still would need to copy them to your Computer,