I feel ashamed and do not want to look greedy if I claim mut'ah. Should I claim it?

Claiming mut'ah is not greed; it is a right Allah has set as an honour and a consolation for a divorced woman. Mut'ah recognises the years you gave to the marriage. It is also often important capital for starting a new life, especially if you gave up work for the family. You can claim it with dignity: through the court, without insults and without exposing your ex-husband's faults in public. If you truly choose not to claim, make sure it is a decision made calmly, not out of pressure or guilt. Talk it over first with someone you trust. See women's rights.