I had Botox and didn't experience any such side effects. We've had lots of folks here get Botox and I don't recall any of them having those severe side effects either. In most cases, the procedure is largely uneventful, and if there is discomfort, it's usually localized.
That having been said, yes it's always possible to have a serious allergic reaction (i.e., anaphylactic shock) to any substance, and Botox is no exception. But it's extremely rare and I wouldn't worry too much about the possibility of an allergy (just my opinion). That risk exists with every single thing you eat or touch every day.
The other thing the literature might be referring to is the isolated cases where Botox travels outside of the local area where it was used. That's an exceedingly rare complication but it's a risk that does exist. Botox is one of the most powerful neurotoxins -- the reason it works is because it totally paralyzes muscles. So if it were to somehow travel outside of the injection area (for example to your muscles that control breathing), then it could have some real nasty effects. This is also exceedingly rare. I'm a pretty hardcore worry wart and I was mildly concerned about this going in, but I knew the risk was so low that I didn't dwell on it much. I figured the odds of being in a fatal car accident en route to the clinic were higher than having Botox spread where it shouldn't
To be perfectly honest with you, I would not worry about the Botox at all. The fissurectomy will likely (almost guaranteed) cause considerably more discomfort in the long run, and IMO the Botox will be a breeze by comparison. (Note though that I've never had a fissurectomy so I'm not speaking from direct experience there.)