It’s good that you brush and floss, and it might be good to do these again after eating the meat. Chewing tough meat fibers can work bits of meat into the spaces between your teeth.

Sore gums suggest that your brushing and flossing need to gently clean along the gum line and at the base of your teeth. Also brush the gums, to massage them and stimulate blood flow.

If your work and social life permit, you can help accustom the tissues to this work by chewing a wad of chewing gum well beyond the point where it loses flavor and softness. This can build up your jaw muscles (which will make your dentist think you’re grinding your teeth), and it will toughen the gums and tooth sockets. “Self-limiting” pain from this chewing should keep you from doing damage.

If the soreness persists longer, see your dentist.

http://medianet.info/2018/02/23/what-to-do-if-your-teeth-hurt-from-eating-meat/