The honest framing is that this is very common, usually self-limiting, and occasionally the presentation of something that is not self-limiting at all — and the differentiating features are specific enough to be worth knowing.
The gallbladder signal tracks the rate of weight loss more than it tracks the drug. Rapid mobilisation of adipose tissue increases biliary cholesterol saturation and reduces gallbladder motility; that combination is lithogenic whether the loss came from a drug, a very-low-energy diet or bariatric surgery. The drug contribution on top of that is present but smaller than the rate contribution.
More usefully, distinguishing an injection-site nodule from an infection: a nodule is firm, non-tender or mildly tender, not warm, not expanding, and appears within a day or two. Cellulitis is warm, tender, expanding, and often accompanied by systemic features. A sterile abscess sits between the two and is fluctuant. Warmth plus expansion plus fever is the combination that stops being a forum question.
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 limitation of the timing heuristic is that it works well for common events and poorly for rare ones, which are precisely the ones that matter most.
Fix the fixable causes first — fluid, electrolytes, sleep, intake — before concluding that the compound is responsible.