Well he could have a "period" in that I suppose hormonal peaks and valleys from his therapy could cause psychological distress kind of like PMS?

Just you know, not on a monthly cycle.
Serious (aka. actually meets diagnostic criteria) PMS is only experienced by 3-8% of women.
[1] Another study found that only 4.1% of women had it, with a further 8.1% having moderate PMS (only 1-5 symptoms, not meeting diagnostic criteria), and nearly 3/4 didn't even have sustained symptoms (e.g. they didn't get it every cycle).
[2] The largest number reported is only 20-32% of women, using the broadest scope of meeting any symptom at all at any time.
[3] And this is based on a plethora of different symptoms, some common ones include "headache", "fatigue", "bloating", "anxiety", "backache", "self-deprecating thoughts", "hunger", "increased/decreased sex drive", "sadness", and "insomnia". No clear cause has been found, but it's more common in women who have had kids and the treatment is anti-depressants – not hormones.
[3]
[1]
https://www.ncbi.nlm.nih.gov/pubmed/24161307
[2]
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3196060/
[3]
https://www.ncbi.nlm.nih.gov/pubmed/22010771
So, PMS affects a vanishingly small percentage of the female population, and even when you count every woman who has any symptom at all, that's only about 1/5 of the population. The symptoms commonly associated and used for diagnosis might surprise you because they're not stereotypical when people talk about PMS – when they say 20% of women have experienced a symptom of PMS, it's probably not the crazy mood swings it's stereotyped as and is instead something like "headache" or "fatigue". (Hell, with those symptoms, some men might think they could have PMS.) Not to mention, the broad range of symptoms, their non-specificity, and the lack of ability to tie it to a clear hormonal cause would tend to suggest that for most of the minority of women who experience it, it's psychosomatic or a social contagion and not real. That it affects women with kids and is treated with antidepressants suggests it might be tied to post-partum depression as well as social pressures of raising a family – citing your period and a headache can give you a break from responsibilities or an excuse for lashing out.
The takeaway is, trans people claim they're experiencing PMS because they think that makes them 'like a real woman' when the vast majority of women don't actually experience it and those that do aren't getting the crazy mood swings they're thinking of. It's actually kind of insulting to think that becoming irrational and emotionally unglued means they're acting like a woman.
Transwomen's idea of femininity and womanhood often come across as an incel's idea of what women are like. Reminds me of a tranny who said that she's sure she's got a female brain now that she's taking estrogen because she cries when she sees baby photos. Like every woman's behaviour is ruled by their dusty wombs yearning to fulfill their purpose, and throwing tantrums every month when they're thwarted.