You definitely need a cleaning done as soon as possible. There is a lot of calculus build up leading to gum inflammation and pain. It also looks like you have a cavity on one of your front teeth, so I suspect there might be some other issues as well. Antibiotics might slightly help, but only for a while, because antibiotics is never a solution to any problem. The underlying cause needs to be addressed.
Try rinsing with a disinfectant mouthwash in the mean time, or phone around to see if you can get an appointment at another dentist for earlier.
You can also use any anti-inflammatory medication to assist with the pain.