Just an FYI.
We were in Luzern several years ago when something similar happened. We went to the train station (seriously) where there was a 24 Emergency Room. It was Friday, we were there about 45 mins, it cost about 150 CHF (including 3 medicines given to us by the doctor themselves), and we were out in 45 minutes. We were very happy with the service, doctor, et al. Amazing really. Friday night in a US ER might have run into the next morning and cost a lot more than 150 CHF for all we received.
Never been to the Geneva train station but either check online or ask your hotel receptionist.
A better trip for you guys!