You may have heard about the phenomenon of a "cervical lip". Since I mentioned this above, I feel I should talk about it for a moment. There is a lot of discussion in the birth world about what to do with cervical lips.
A cervical lip can occur when a portion of the cervix doesn't fully dilate and efface. This can happen for a variety of reasons, but the most common are a baby that is malpositioned and its head isn't putting pressure squarely in the center or the cervix, or because a mom remains immobile in bed placing pressure only on one side of the cervix. The cervical lip will be a bit thicker than the rest of the cervix. They can occur anywhere, but are called "nterior lips" because when the baby's head is descending during 8-10cm dilation, feeling behind the cervix to find a posterior lip is nearly impossible. The most common locations would be at 11 and 2 if you pictured the cervix as a clock.
It's commonly believed that if a woman pushes before full dilation (which is the reason given for performing routine vaginal exams), she will tear her cervix. However, there is simply no research or even enough anecdotal evidence to support this. You also have to consider all the women worldwide giving birth without cervical checks: if no one's fingers are in your vagina, then you won't know if you have a cervical lip or not, you'll just push when you feel like it's time.
It is possible for the cervix to swell closed by a few centimeters if it becomes too irritated by manipulating it or unequal pressure. To avoid this, listening to your body is key. This usually happens when you lay down during labor and staying upright and mobile cannot be stressed enough.
If a swollen cervix or lip occurs, most midwives agree to not put pressure on the swollen portion. Relieving pressure by switching sides can be beneficial. Some midwives use ice or will even push back the lip over the baby's head.
Usually, the best rule of thumb is to let your body tell you what to do: if it hurts to push, don't push! If it feels good, then push!