Cervical incompetence is a diagnosis suspected clinically in women who had second trimester miscarriage in the past (mostly between 12 - 20 weeks). This is usually painless and spontaneous.
The diagnosis is also based on ultrasound scan findings wherein (as you have correctly mentioned in your query) the internal cervical os is open and there is funnelling of membranes in the endocervical canal. These two findings suggest likelihood of either mid-trimester miscarriage or preterm labour. Putting in a cervical stitch (a suture around the cervix i.e. neck of womb) does successfully avoid these possibilities.
Unfortunately with the information you have provided I do not see any reason to justify the procedure you had.
There is no need for bed rest. You can carry out your routine activities. However, you should not do any rigorous activities such as lifting heavy weights / objects, gym etc. It also depends on the nature of your job. You may carry out office-based jobs without any problems. Travelling in auto / car also should not be a cause for concern.