Is it possible that many people will experience blood clots or other severe reactions months after taking the Covid vaccine?

It's a rare side effect of ONE vaccine, but it is a very COMMON side effect of getting Covid.  Why wager on something with 300,000 to 1 odds against you?

As far as I am aware no link between having one of the COVID-19 vaccines and subsequently having a blood clot has been established. The number of people who have had a vaccine and subsequently a blood clot is miniscule; far less than you would anticipate if the vaccine were causing them. Secondly, the number of people who have had a COVID-19 vaccine and then a blood clot is a lower proprtion of the population than the number of blood clots that generally occur in a year. That is another clue they are probably not linked. Thirdly, there seems to be no biological reason why a COVID-19 vaccine would cause a blood clot.

Vaccines are designed to work straightaway. They stimulate your immune system to produce a response to the disease against which you are being vaccinated. Consequently, if you were to develop some sort of undesired response to the vaccine it is going to be shortly after the vaccine was administered or after a booster dose. There should be no serious side-effects developing a long time after the vaccine.

It's rare because it happened seven times out of several million doses.

there is no *the* vaccine

No bloodclotting-issue has arisen with the Moderna or Pfizer-Biontech vaccine

a few people have had such issues after getting the Astra-Zeneca or the Janssen vaccine

No. The few rare cases have occurred ONLY in women under 60, so there's no risk to men. That makes the chance less than 1 in a million. Compare that to blood clots with birth control pills which is 1 in 1000.

If a million people got the vaccine, I would expect 1 or 2 to get blood clots from it.

If a million people DON'T get the vaccine, I would expect 2 or 3 to get blood clots from Covid.

As for "is it possible" ... it's possible that some of them will turn into green elephants in 2 weeks or so.

anything is possible. Could you be hit by lightning tomorrow? also possible. Should you obsess about being hit by lightning on a clear day?

Many people: no.

Its unlikely to cause blood clots after 2 weeks.

Millions of doses have been administered over several months.

People get blood clots for numerous reasons. A 1 in 1 million chance it will happen from a covid vaccine is actually better odds than one occurring without it.