What Causes Painful Swelling Below Left Ear?
An enlarged lymph node more likely.
Detailed Answer:
I read your question carefully and I understand your concern.
I do not think that it is a case of swollen carotid artery, the carotid artery is not located where you describe it and anyway it would be a pulsatile mass.
Given your description the most probable nature of that swollen and painful area would be an enlarged lymph node. Most commonly they are harmless, due to some local infection (tooth, skin, throat etc) and if the infection subsides they gradually subside as well. Rarely though are they a sign of blood tumors or more serious infections.
So as you can see it is hard to determine with certainty whether it will go away as it depends on its origin. For that reason if it persists or increases with signs like fever you should be seen, it should be directly examined as well as some blood tests may be needed to test for infections, inflammation markers, tumor etc. Whether treatment will be needed or not depends on the findings.
Another possibility would be a muscle strain or arthritis, but that is not typically associated with swelling, so since that is the case less likely.
I remain at your disposal for other questions.