The word "conflict" is usually used for situations that last for a significant length of time.
"World War II was a lengthly conflict."
But "confrontation" suggests that the problem occured at a specific point in time.
"There was a big confrontation between John and Paul this morning."
These are not strict rules, but I would choose "conflict" as you are referring to something ongoing.
I'm not a teacher.
Student or Learner