In this area there are three common reasons for swelling.
One is there is a lymph node under the jaw hinge that can swell when the dog's system is fighting off an infection.
Another possibility is that there is a salivary gland that can get blocked and swell.
And finally this is the area where there is apt to be swelling if there is a dental infection in rear teeth or in the back of the mouth.
Splinters of bone or wood can cause damage and infection in the rear of the mouth as can a broken tooth or dental disease.
With all the drooling that could be nausea but it could be a sign of an injury in the mouth too.
You are going to need to see a vet with him for help but the question is should you see a vet today or can it wait until your vet opens.
This info may help you decide -
If your dog might have gotten into anything toxic (including toxic plants), appears dehydrated (see if a pinch of skin over the shoulder blade stays stuck in a tent form or flows back down normally when released), has a rectal temp over 103.5F (normal is 100.5-102.5 Fahrenheit or 38 - 39.2 Celsius), has gums or tongue that look white, blue, gray or yellow tinted where they are normally pink, has a slow color refill if you press on a pink area of gum or tongue, cannot eat or drink, is having difficulty breathing, or is becoming more lethargic and non responsive to you or is otherwise getting worse as time goes on then you may want to get the dog in to see an emergency vet if one is available in your area.
This site may help you locate an emergency vet if you need one
Otherwise you may want to see your vet first thing when they open.
Hope this helps you!