I'm sorry to hear about your little dog.
The area of these swellings are where lymph nodes are located (specifically, the submandibular lymph nodes). Lymph nodes swell for several reasons: infections, inflammations, and cancers being the most likely.
The lymph nodes in this area are the drainage area for the head region, and often things like tooth infections and abscesses cause this problem. Same with the other lymph nodes: more localized infections cause those specific lymph nodes to swell. You can check other obvious areas of lymph nodes for swelling: probably the easier for you to detect would be in the back of the legs (like behind the thighs).
If these too are swollen, this is a systemic problem. If not it may or may not be a systemic problem.
Due to your Yorkie's age, symptoms, and amount of time its been going on, don't put off a vet visit long. Even though this still may be just infectious, antibiotic treatment should start right away. The coughing is likely due to the compression of these glands against the trachea.
Cancer is always a possibility here as well, but great strides have been made in the fight against it. As with any illness, quick diagnosis and treatment are your best bets.
I wish there were something you could do from home to help, but unfortunately this is a bigger issue than that. As long as he's breathing well and acting like himself besides the cough, it can certainly wait until your vet opens, but don't put off a visit past this coming week, so quick treatment can get started.
Let me know if you have any further questions.
No, these problems, having been around for years, would have nothing to do with his lymph nodes now being swollen.