If the mucus is only for one time or just one day don’t worry about it. After a bad case of constipation losing some mucus is quite normal. My only suggestion is not to get that badly constipated. I, myself, if I don’t have a BM one day take an enema the following day to avoid more serious problems. And, yes, you can take enemas before, during and after menstruation.
Some women take an enema before their menstruation to try to minimize their PMS symptoms. Taking an enema during your period could alleviate minor discomfort of menstruation.
I don’t think that you have an obstruction or a polyp. What you are feeling is most probably residual effect of your constipation followed by diarrhea. I would make sure that my diet was clean, lot of veggies, low in red meat and carbohydrates, and I would take for the next few days one or more daily cleansing enemas,