Katie, even though most vets are closed on weekends and holidays, if you live in a larger city, there are often emergency vet clinics that operate when vet offices are closed. We have a few in the area I live in and they have a vet on duty 24/7 from about 5 pm each day until around 8 am in the morning plus all weekend. Try checking the yellow pages for veterinarians and you may find one where you live. Ours is called an "after hours vet clinic".
Try the internet, googling "wildlife rehabilitators" for the state in which you live.
In the interim, although I know nothing about rehabbing a swan, I know it needs to be kept in a warm and quiet environment.