Sounds like probably trypanosoma to me.

Quitting HRT due to having health issues after adding progesterone to HRT

This sounds to me like trypanosoma and magnesium deficiency. 

Trypanosoma is a parasite. Allergies are promoted by parasitic infection. I don't remember the explanation but asked my very sciency son "If absence of evidence is not evidence of absence, how will we know when my trypanosoma infection is actually gone?" and he did some research and told me "When your allergies are resolved because parasitic infection promotes allergic reaction."

Trypanosoma infects the heart and causes heart issues. Magnesium deficiency promotes arrhythmia.

I would suggest they keep their HRT drugs. HRT is probably helping this person combat trypanosoma and if they get a positive diagnosis and treat for trypanosoma, they may wish to go back on HRT soon.

Sex hormones are part of the immune system and most likely getting the right hormones for their body boosts the immune system and that's why some people report symptoms following the start of HRT: Because their body has begun battling long-standing issues it couldn't battle previously.

I have a long, long history of ear infections going back to at least age three. I went on birth control pills at age seventeen and for months after starting birth control pills, I had huge, painful carbuncles in my ears swelling them shut and causing neck pain until it drained. This was most likely long-standing unresolved infection in my ears getting cleared out more thoroughly because I have a genetic disorder and permanently compromised immune system.

Zithromax helps with trypanosoma and is probably cheaper and less toxic than most antiparasitic drugs. Levaquin too.

It takes a long time to treat trypanosoma but one can see improvement quickly. There's lots of information about trypanosoma on my health site. This is the start here piece for trypanosoma on that site.

So question for myself: Why after progesterone started? What does estrogen do to the immune system versus progesterone and is this significant for either promoting magnesium deficiency or combating trypanosoma in specific?

Footnote 

Magnesium deficiency can happen rapidly and can be a consequence of fever. Depending on where they are in the world, the start of progesterone may not be causative but may merely coincide with the start of hot weather.