Yes, unfortunately you can get an infection at any time, and post-surgical infections are not at all uncommon. Anytime an incision is made into any part of the body, it's possible for bacteria to invade the tissues and cause an infection. Signs of infection include fever, swelling, tenderness, reddened areas, and pain.
Because the jaw area has a lot of lymph nodes, a tooth or jaw infection can also cause swollen lumps or nodules in the neck, under the armpits, or even occasionally in more distant areas of the body such as the groin. This happens because bacteria that get into the lymph system cause the immune cells that are normally present inside the nodes to go into disease-fighting mode, which creates swelling and sometimes pain.
If you have any of the symptoms of infection, you should call your doctor or dentist immediately and get checked out. Infections in the tissues of the mouth can be dangerous, as some of them can actually cause bacteremia, a type of infection that can cause heart damage if left unattended. If you have to wait a few hours, you can try applying hot compresses to the swollen area. Rest and good hydration are also important in helping your immune system do its work.