Concretely, look at the placebo arm before concluding anything about attribution. The placebo-arm rates for most of these events are not small, because the events themselves are common in the underlying population.
The telogen effluvium timing signature is the diagnostic feature: hair enters the shedding phase two to four months after the insult, so shedding that starts at month three of rapid loss and peaks around month four to five is the expected pattern. Shedding that starts in week two is not telogen effluvium and warrants a different question. In either case the follicle is not destroyed and regrowth is the rule.
On the detail: constipation outlasts the nausea because it has two causes and only one of them resolves. Gastric emptying accommodates over weeks; total intake, and therefore stool volume and the osmotic load reaching the colon, does not recover until intake does. This is why fibre alone can make it worse — you add bulk to a system that is short of water and short of motility.
Telogen effluvium following substantial weight loss is documented independently of any pharmacotherapy, which is the cleanest argument that the rate of loss rather than the agent is the primary driver.
The caveat that actually matters: this is pattern recognition from published data, not a clinical assessment of you. Anything severe, persistent or accompanied by systemic features belongs with a clinician the same day.
If the timing does not fit the escalation, look for another explanation before settling on the drug.