Can a law firm change my title without increasing my pay?

I work for a law firm and we had two offices in the city. The office I worked in was moving into the other we have. I was a receptionist however due to the move my position was changed to a position with more responsibility since the office already had a receptionist. I was not offered a pay increase, they advised since they had to place me somewhere and even though the position usually pays more then my old position there will not be a pay increase. Can they do that, change my title but not increase my pay? If someone new where to come in a start my position they would offer them more. I also found out the receptionist at the new office we moved into is getting paid more then I am, I have worked in this company a little over a year since she has we both at one point had the same title, now my title has changed to one with more reasonability and she still gets paid more then I do. I really need help with this situation.