Dog has sudden lump under eye. Sting, abscess? How urgent is vet?

It could certainly be a sting, as the area does appear reddened. I would also consider a tooth abscess very likely as well, as they often appear somewhat suddenly and cause swelling just under the eye. If Amiga has dental disease - and you should be able to tell if she will let you look in her mouth on that side, in the back - there's a high possibility. Watch her closely for signs of a serious reaction in case this is an insect sting, as some dogs (like people) can have intense inflammatory responses. Signs would be difficulty breathing, sometimes accompanied by vomiting and diarrhea, and collapse/weakness. The thing that is concerning is that from the pictures she looks to be in pain, based on the way she is squinting her eye. I would call the vet again to see if they can get her in earlier, or try a different vet - if it's a tooth root abscess it could be quite painful. The other possibility would be a mass/tumor of some type, but that seems less likely since you've just noticed this today.