My understanding is that when you're constantly busy, your stress hormones are helping to protect you from getting sick. When you suddenly get a rest, your body is weak and tired and the stress hormones quickly go away, leaving you very vulnerable to actually get an infection. You're really getting sick, it's not as if when you were busy the body just ignored infections that were happening.
you are completely wrong. The central hormone in response to stress is cortisol. here is the wiki page: https://en.wikipedia.org/wiki/Cortisol#Immune_response.
I will quote some important excerpts.
Cortisol prevents the release of substances in the body that cause inflammation. It is used to treat conditions resulting from over activity of the B-cell-mediated antibody response.
Cortisol can weaken the activity of the immune system. Cortisol prevents proliferation of T-cells by rendering the interleukin-2 producer T-cells unresponsive to interleukin-1 (IL-1), and unable to produce the T-cell growth factor (IL-2).[11] Cortisol also has a negative-feedback effect on interleukin-1.[12]
Cortisol and the stress response have known deleterious effects on the immune system. High levels of perceived stress and increases in cortisol have been found to lengthen wound healing time in healthy, male adults. Those who had the lowest levels of cortisol the day following a 4 mm punch biopsy had the fastest healing time.[26] In dental students, wounds from punch biopsies took an average of 40% longer to heal when performed three days before an examination as opposed to biopsies performed on the same students during summer vacation.[27]
This isn't really a difficult concept and certainly doesn't need an expert. In fact, it's actually covered in most high level (AP/IB) highschool courses (MCAT has it and MCAT only tests the truly entry level knowledge).
Now,
your stress hormones are helping to protect you from getting sick
although this statement sounds like agreement with op, it is actually hilariously ridiculous. You are claiming that stress hormone not just suppress symptoms but actually fight infections. Firstly, the idea that hormones themselves fight infections is ridiculous cause they are signal molecules.
Secondly, if cortisol is telling the body to fight infections, where does the energy come from? the immune system is an incredibly energetically expensive system because it fights infections with almost cancer like proliferation (In fact, most immune suppressant drugs for auto-immune disease or graft vs host are actually just chemotherapeutic agents). stress response is about making a choice about energy (sugar) expenditure. If you can power both the immune system and the muscles/brain at the same time, you won't need 2 modes, just use both all the time. (have your cake and eat it too).
In reality, if you read the metabolic effects of cortisol, it basically breaks down your entire body (stored glycogen, fat and protein) to increase your blood sugar so your muscles and brain can have enough energy to run because you are running away from a lion and could die in the next minute so burning your body up to survive is a good idea. No, it will not spend any energy preventing infections because you might die in the next minutes and a festering infection is a worry weeks away.