Good question. Based on everything you have said above I would tend to agree that you have reached a temporary plateau in training load. Here are some suggestions to help you get through this period without having to resort to quitting your teaching job or wearing a Hazmat suit in class,
MORE MODULATION IN TRAINING LOAD: Make sure that your easy days are truly very easy. Reduce intensity but not volume there. Stay well below your AeT in long run/hikes.
CUT VOLUME 50% IN RECOVERY WEEKS: These weeks should be focused on getting recovered not on training. Be aggressive with recovery techniques. Sleep lots etc.
You can’t get away from the stress of daily life. Training close to your current load limit WILL lower your resistance to illness. If you are getting sick often then this is your body telling you that you are close to that limit.
I’m going to try to get Scott Semple to add comments here because he used to have this problem but is managing training and sickness much better than in the past. He may have some other insights.