You’re so right in that vaccines and boosters are meant to help prep the immune system and set up antibodies for any future exposure to a specific bacteria or virus. It doesn’t boost the entire immune system.

People who have compromised immune systems still have a working defense system, it’s just not as robust as it would be otherwise because of chronic illness, medications, blood cancers, etc. So vaccines aren’t contraindicated.
Their blood still contains the critical cells for launching an attack against an invading bacteria or virus, just not in the usual quantities and the response may be slowed because of the compromised innate immunity.

There is also acquired immunity, also called adaptive immunity, which uses T-cells and B-cells when invading organisms slip through a first line of defense of innate immunity. It’s like calling in the big guns in a battle. So even if the system is suppressed the vaccine can still help create some adaptive immunity for a particular disease. That will depend on compromised level of the system. Granted, some people are severely immunocompromised and a vaccine might not trigger much response. They may need an extra dose as in the case of the Covid 19 vaccine. Or the current influenza for adults over 65 for instance. It is a heftier dose of the usual vaccine because as we get older our immune systems weaken naturally.

But sometimes, a vaccine, any vaccine, can also cause an autoimmune response and launches an attack against the body such as your flair up of the psoriatic arthritis.

Often it’s treated with a quick burst of steroids to calm the overactive immune response and things go back to normal. . Have you seen a doctor regarding your flair up?