Yes, it is possible for a swollen lymph node to remain swollen for up to a month after a cold, especially due to pregnancy congestion. Swollen lymph nodes can occur during and after an infection, illness, fatigue, or stress. It is recommended to avoid touching or massaging the swollen lymph node. As long as you are experiencing a runny nose, the swelling may persist for up to 4 weeks. If you have any other questions, feel free to ask a healthcare professional for advice.