Some are afraid to get Long Covid from the vaccine, or were a bit sick after the shot and are concerned.

Getting a bit sick is a normal reaction to any vaccine that can trigger an immune reaction; your body is learning how to fight off the nasties.

Getting Long Covid from the vaccine is possible but rare, while getting it from, well, The Virus, is more common. The vaccine may also protect against Long Covid.

Research is still being done.

https://www.science.org/content/article/rare-cases-coronavirus-vaccines-may-cause-long-covid-symptoms

https://www.health.harvard.edu/diseases-and-conditions/vaccination-may-protect-against-long-covid 

 But is the vaccine any better than getting the real thing? Research will take a long time to find that out too. And you still get it after the vaccine.