Some teeth get meat lodged between them and that can be painful. Doesn't happen too often. I used to get those little interdental brushes for dislodging stuff instead of using floss.
Receding gums has a lot to do with brushing teeth too hard too. Trying to teach my kids to brush lightly. For this, electric toothbrushes are helpful as some start flashing or buzzing more if you press too hard etc.
Also, try to avoid brushing teeth in the half hour or so after food. Any acid that's produced gets nice and worked into your teeth and gums by the toothbrush. Rinse well before brushing if unavoidable.
And don't rinse the foam away. Keep it on your teeth as long as possible.