Hi thanks for your question.
you had ureteric stone ,which has passed into bladder,this is not due to medicine but due to normal peristalsis
The burning sensation your having while passing urine is due to urinary tract infection
due to stone.
Obstruction while passing urine is also due to obstruction to urinary outflow by stone,that is why you need to pass urine twice.
The stone is 11 mm,chances are that it may pass through your urthera ,but if didn't you may need operation.
There is no medicine which can help in passing your stone.
Hope this answers your question.