My brother had that (quite legitimate, really) concern. So he delayed vaccination. Now he has Covid. Doctors talking of amputating his toes because of blood clots. Death is not the worst thing to be feared in this.
Anecdotally, I know someone who got the vaccine, and dropped to the ground of a heart attack 3 days later - no prior history of any heart issues or hypertension. Thankfully, he was near an EMT unit that had to bring him back.