Oftentimes we feel worse before feeling better when treating illness. It's analogous to a pimple coming to a head. It festers and hurts before it pops.

As our immune system fights it can cause low-grade fever.

yep that's part of the immune response, raising temps to kill pathogens and the whole process can be a source of pain. This theory also proposes that the toxins of the mass die off of pathogens can increase toxic levels and pain as well.
Don't you ever wonder where the 10 million (in some folks) dead virons go to?
This is a debatable theory and many discredit it. As it does not prompt any action but just offers up an explanation of feeling worse before feeling better, I thin it's interesting to ponder.

I think they dissipate into our blood stream and if we drink lots of water we pee out the dead pathogens...

I think it's a little more complicated like that; not a case of just down the kitchen sink. The body has to know how to identify and process things that it doesn't want. There are many pathways for this process, spleen, liver, kidneys,etc. Yes eventually they would be excreted but in the meantime this theory is saying that they create a noxious toxic state until they are eliminated. Just like drugs can cause so many ill effects, so potentially can "die off" pathogens until they exit the body.
It's just a theory, something to ponder, a possible other explanation why we feel poorly while we are getting well.
I leave off now.

thanks for making me think guys...have not done too much of that lately it's like my mind went on vacation...a long one...