Asking for help when choosing appropriate statistical test

Hello there

Currently conducting a study on the impact of palliative care support in Heart Failure patients.
I have collected the number of admissions of heart failure patients over the course of 2 years. I am now trying to compare the difference between those who had palliative care input and those who didn't.
There is a nominal difference between the number of admissions. What test is most appropriate to determine if the difference is statistically significant?

Apologies if it is a really simple question, I have been through various decision trees and online questionnaires but cant seem to find one that fits.
You could handle this with a simple 2 proportions test, or with a distribution comparison test (do you have a number of admissions for each patient ? Between 0 and how much)
aprox 600 sample size.
The number of admissions varies between zero and I believe the maximum is 14
I intend to compare the number of admissions at 3 6 and 12 months following first admission (collected data for all of these)