The standard is to run a Phase I trial to identify any major safety issues in a small population, and identify the appropriate dose to use in later trials, as well as gather data about potential efficacy. Phase II is an extension of Phase I - enroll more patients, check for any new safety issues at the determined Phase II dose (from the Phase I trial) in a broader population, as well as more rigourously look at efficacy. The last step is to identify an appropriate clinical trial efficacy endpoint, then enroll tens of thousands in a Phase III placebo-controlled trial where patients are randomized to either vaccine or placebo, and then monitor safety and for events triggering the primary endpoint. Safety follow-up will often run for 2+ years, but due to the nature of vaccines, almost all adverse events of interest will occur temporally close to the vaccination date(s).
The standard has been followed. Timelines have been compressed due to the fact that there is a pandemic, but I wouldn't say that dangerous shortcuts have been taken.
As for the incidence of adverse events, that data is reported - you're welcome to take a look at it:
NEJM publication:
https://www.nejm.org/doi/10.1056/NEJMoa2034577
FDA advisory committee meeting and materials (including the data - see the briefing document PDFs at the bottom of the page):
https://www.fda.gov/advisory-commit...0-2020-meeting-announcement#event-information
Your one post about a single subject's experience is not representative of the trial data. We also know how to control temporary fevers - you could pop a Tylenol if you had a fever.
Anyway, there is no risk-free vaccine. If there was no pandemic or serious risk of coming down with COVID-19, it would be pretty stupid from a risk-benefit standpoint to take the vaccine, since it would be all risk and practically 0 benefit. But there is a pandemic, with a virus that seems to cause long-term damage in some that survive, so the risk-benefit profile has shifted greatly in favor of the vaccine, even if a small percentage have a fever