Cost coverage for StroVac?

Hey.

I suffer from chronic cystitis.
However, not 2-3 times a year, but rather 2-3 times a month.
In December it lasted a whole month and in January alone I was in the emergency room three times because of it.
Of course, this also causes chaos at my school. At first, I often came in late because I drank so much in the morning and took painkillers until I felt somewhat better, and I left early as soon as I got chills and pain that was unbearable.
Now in winter I can't manage it anymore.
As soon as I get out into the cold, I get a bladder infection.
Last time it affected her kidneys, and this morning it started again.
As I mentioned, I'm a student, so I don't really have any money of my own, and the vaccination isn't usually covered by statutory health insurance. However, neither my gynecologist nor my urologist know anything about it, and in the emergency room, I was strongly recommended to get vaccinated.

Do you think this is something we can discuss with our health insurance company, or does that seem impossible? It's really starting to get tough for me that I can't manage school anymore because of this, and it's also starting to take a toll on me mentally.