Can the doctor induce me for an irritable uterus at 37 weeks?

No. Really should not. At 37 weeks the baby's lungs may not be mature. If you have true labor then we would not stop it. But if you have irritability then better to let natural labor occur.
No. Induction of labor should not be done before 39 weeks unless there is a clear medical reason. As long as the pregnancy is otherwise normal, an irritable uterus would not qualify as a reason where the risks of early delivery would mean it is safe to induce labor.