If you know for sure she does have bad teeth, then teeth would be the first thing I would think of. If she has an
abscess under a tooth, it would cause quite a swelling. And it would be likely to affect the nearest lymph nodes, and cause swelling there too.
There has to be a solution found for the vet's inability to examine her mouth.If she is that bad when examined, she will have to be sedated fully, for the vet to take a look. But it is wise to do that I think.