You're being irrational. It's true side-effects can take time to manifest. It's also true that problems due to the disease also can manifest. Taken together the fact that _something_ can possibly happen in the future gives you _no_ information today. For example, one of the side-effects of the vaccine that might manifest might be that you're _healthier_.
So yeah if you take the possibility of negative side effects, but not positive side-effects, you are being irrational. Said in another way, if you are taking statements devoid of information ("something can happen with some likelihood in the future"), you are being irrational.
All actual current information points overwhelmingly to the fact that the disease (even considering that not everyone will get it) is much worse than the vaccinations. That is information. That information points to one conclusion and it's not "wait forever and see what happens".