As far as I know, no vaccine has ever shown long term side effects. If there are side effects, which does happen at low rates for almost any vaccine, it tends to happen within hours, days, weeks at most. The current COVID ones have been used for six months and tested for amount the same amount of time before that. Yes, that's faster than normal (although fly is fairly fast, too, every year), but they simply worked harder and did things in parallel where possible. No steps were skipped. So I wouldn't worry at all about long term side effects.
However, side effects that show more quickly are possible, but happen at levels of about 1 : 100,000. In many parts of the world about 1 : 1000 people has died of the virus the past 18 months. (Mostly the elderly, of course, but not exclusively.)
The side effects tend to happen more often with younger people while the risks of not
getting vaccinated are lower for younger people. So a few months ago, before the delta variant, the logic was that people under 30 or so should probably not get the AstraZeneca vaccine, which had shown those ~ 1 : 100,000 side effects. Not 100% sure, but I think things are similar for the Johnson&Johnson vaccine, which is a similar type vaccine.
But the Pfizer and Moderna vaccines have much lower levels of side effects and the virus is coming back with a vengeance. So I'd take the vaccine. (I actually took AstraZeneca rather than wait for Pfizer.)
Remember, drugs that we take all the time also have side effects, in rare cases serious ones. Tylenol, for instance:
Tell your doctor right away if any of these rare but serious side effects occur: fast/slow/irregular heartbeat, seizure.
A very serious allergic reaction to this drug is rare. However, seek immediate medical attention if you notice any symptoms of a serious allergic reaction, including: rash, itching/swelling (especially of the face/tongue/throat), severe dizziness, trouble breathing.