Can one have bilateral posterior cervical reactive lymph node swelling on the neck after wisdom tooth extraction? if so, how long does it last for?

Yes you can: This is not uncommon. Duration varies. Have your surgeon check you, .

How long post-op?: When were your wisdom teeth removed? Do you have any pain at the site of the wisdom teeth? How did you learn you have bilateral posterior cervical reactive lymph node swelling? If your physician saw you, did you ask about the relationship to wisdom tooth extraction? Lymph node swelling which originates from an infection can either subside or they can fibrose (scar), which is not abnormal.

Monitoring Centers: Lymphatic system absorbs/carries things too big to go into the arteries/veins like bacteria eaten by white cells and digested food. Lymph nodes "taste" the lymph for anything bad like bacteria/viruses/cancers, etc. When it detects a problem, it alerts the immune system and your body reacts. They enlarge in response to the inflammation they create when they react. They shrink when all is well.