Mouth outer lining sore?

Dear Vets, yesterday I noticed a sore on the left side of my dog’s mouth (or what appears to look like one?) while at the park. Her stool was very soft as well. She is 8 years old, Pomchi mix, good health (did a blood test 1-2 weeks ago). Plaque build-up from age. Another thing that concerned me is at the park she was chewing on sticks and there was blood  on the stick (and on the right side of mouth). Hasn’t happened before. I mashed her kibbles and didn’t let her chew on anything hard for the day, then tried to do a water + salt swab on the sore. Today she had diarrhea (once). Energy was fine on the walk and she ate rice and chicken as well as drank water. About 10 days ago i also noticed a small scab from a bug bite at the top of her head (not sure if related). Any advice on what it could be and how it could be treated or how serious the sore may be?

Hello!  It's very difficult to tell what's going on from that picture; I can see what appears to be a lump close to the corner of the lip.  If it is a lump, it is possible that this could be cancerous (benign or malignant) or inflammatory  eg a sting, abscess or infection.  Vitiligo or impetigo may also be possibilities.  It is curious that the pigment changes, so your vet may want a sample.  We would advise presenting the lump in order that they can examine it properly and from there make a judgement as to what is required.   As for seriousness, from what I know at the moment, the range of possibilities is very broad but your vet will be able to narrow it down.  Please do let us know how you get on.