Congratulations on completing treatment!
Your doctor is right, radiation continues to work just as long as your treatment lasted, and was told 6 weeks. After my radiation treatment in 2011, I still had an enlarged lymph node that the doctor wasn't too concerned about either, saying it was probably necrotic, and waited 5 months to have my post treatment scan, which was clear. Unfortionately, I had loco-regional metatastic recurrence in the lymph nodes about 6 months later, and needed a modified radical neck dissection, which turned out to be a radical neck dissection, and more after that, but my case is not the ordinary. Some doctors like to do a neck dissection for any clinically partial or incomplete responses, and some even a "planned neck dissection" after treatment, in a specified time, keeping the total treatment package under 100 days, which has better outcome than watching and waiting. One of the keys to survival is controlling the lymph nodes.
Good luck with everything.