You were told correctly that the risk was very very very low. However, you should've been given some options at the hospital.
I had a similar circumstance and rushed to the hospital too. This was years ago. I started meds and literally died from the onset of side effects. I recall using the meds for 30 days. However, it's a personal choice. Many people don't opt for meds. They are only affective with 72 hours of infection. You had someone else make the decision for you, like the hospital staff.
Keep in mind that the risk was low. You should turn out fine. However, you should send some form of documentation complaining about the lack providing you with a choice of treatment, if you so desired.