Here are two studies on Bell's palsy (BP): one is looking at rates after covid, and the other at rates after vaccination.
Bell's palsy is a paralysis, typically of part of the face, caused by inflammation around the nerves after activation of the immune system. It is known to happen in rare cases after flu shots. It is usually temporary, but can be painful, so something one would prefer to avoid if possible.
In both the Pfizer and Moderna trials, there were slight increases in cases of BP in the vaccine groups over the placebo groups. The FDA was not convinced that it wasn't just a statistical anomaly, but wrote that it's something to keep an eye on in the future.
This recent vaccine study was done in Israel. They have a centralized health registry, which makes it easier for them to do these sorts of analyses comparing rates of BP in vaccinated vs unvaccinated people in the same time frame (BP rates are seasonal). The researchers took the approach of looking for people with diagnoses of BP and then checking to see if that group's rates of vaccination were higher than those of controls from the general population. They found no difference in vaccination rates in the BP group vs the general population group. They also compared rates of BP to the same time in previous years and found no increase. So it looks like the Pfizer vaccine is not causing BP in Israel, despite its widespread use there.
The other study involves looking at rates of BP after covid. This one was done in the US. They found that 0.08% of people who had covid came down with BP within 8 weeks. That's not a particularly strong association. However, if they looked just at people who had past BP, and then got covid, 8.6% of them had a recurrence of BP after covid. So in those who have a predisposition toward BP, covid does appear to be a potential trigger.
They also did a comparison of rates of BP in people who had covid vs people who had a vaccine, and found that BP was 6.8 times more likely after covid than after vaccination.
This research may be of interest to those with past Bell's palsy who are worried that the vaccines will trigger a recurrence.
Link to studies :
https://jamanetwork.com/journals/jamaotolaryngology/fullarticle/2781368
https://jamanetwork.com/journals/jamaotolaryngology/fullarticle/2781367