Well, the vaccines (plural) were of course going to have an impact on your immune system, that was the point, but I wouldn't call it an "attack". It's more like a wargame, preparing for an enemy you expect to attack in the future; there is risk, but it's a lot less than going into the eventual war without having done any wargames.
We all get exposed to viruses frequently, all the time. If your immune system suppresses them without much effort required, you don't feel sick. If your immune system overreacts, it suppresses them even better, but you will feel sick (from the fact that your immune system is going into overdrive). If your family's vaccination is causing their immune systems to give a stronger reaction to normal viruses, that is annoying, but it doesn't mean the vaccination wasn't a good idea. It's taking on an increased risk of an immune system making you feel sick for a couple days because it overreacted to a normal virus, in order to get a reduced risk of getting hospitalized because your immune system did not take a virus (covid-19, in this case) seriously enough, soon enough.
The immune system is a tricky beast, no question, and unexpected results can happen. But just because your family gets sick, and you don't feel sick, from a normally circulating virus (e.g. perhaps one of the four non-covid coronaviruses that cause 'colds'), that doesn't mean the vaccine isn't working correctly. It just means they're trading a higher risk of a small problem for a lower risk of a much bigger problem.
We all get exposed to viruses frequently, all the time. If your immune system suppresses them without much effort required, you don't feel sick. If your immune system overreacts, it suppresses them even better, but you will feel sick (from the fact that your immune system is going into overdrive). If your family's vaccination is causing their immune systems to give a stronger reaction to normal viruses, that is annoying, but it doesn't mean the vaccination wasn't a good idea. It's taking on an increased risk of an immune system making you feel sick for a couple days because it overreacted to a normal virus, in order to get a reduced risk of getting hospitalized because your immune system did not take a virus (covid-19, in this case) seriously enough, soon enough.
The immune system is a tricky beast, no question, and unexpected results can happen. But just because your family gets sick, and you don't feel sick, from a normally circulating virus (e.g. perhaps one of the four non-covid coronaviruses that cause 'colds'), that doesn't mean the vaccine isn't working correctly. It just means they're trading a higher risk of a small problem for a lower risk of a much bigger problem.