Hello there and welcome to HCM,
The orthodontic wiring on the lower teeth is impinging the adjacent oral tissue which is irritating the tissue leading to redness
,it may also progress to ulceration. consult your orthodontist and check for any loose wiring ends or sharp brackets that are impinging.
At home you can apply dentogel, a antiseptic anesthetic
gel that helps in healing n provides numbing effect. regular mouth rinsing with antiseptic mouth wash or lukewarm saline water gives soothing effect, Start with vitamin b and vitamin c
supplements that helps in quick healing, avoid spicy and hot food, drink lots of water. i hope that helps , take care.