Your story sounds similar to how my daughter reacted when I took the dummy off her at 18 months. Sara screamed at each sleep for around 3 days and then it all just went back to normal.

All I can say is that it does take time to change a habit and eachday will get better. Be consistent and don't give in and let her have it back. Be positive when you are telling her why she can't have it and maybe buy her a new cup that she can look forward to using at meal times.

Good luck