I am sorry your boy has this trouble.
The lump may be a swollen lymph node or he could have an infected tooth root that is not visible to the naked eye.
He could be hyperthyroid which IS a treatable disorder.
Here is a link for more information for hyperthyroidism in cats.
I would recommend starting your cat on methimazole for the first month. After 14-21 days, have a urinalysis and bloodwork repeated to check thyroid levels and make sure NO signs of renal failure are developing. (hyperthyroidism can MASK developing kidney disease. If this is the case, when you start treating the thyroid, the kidney function may worsen).
High calcium can related to renal issues or some forms of cancer like lymphoma.
Swallowing is a symptom of nausea.
If he eats dry food that may be the culprit. PLEASE READ:
Lack of fluid in the bowel also leads to vomiting, Ingested hair can also be a factor.Anorexia for any extended time leads to liver damage and causes nausea and vomiting as well.
I would add some canned or baby food for him
Serve the two foods separately - do not mix them - add a half pepsid a/c tablet, crushed up into the wet food one time a day.
Offer him milk or the water from a can of tuna or salmon for hydration.
Cats are attracted to smelly foods - the stronger the better. If he wants tuna, give it to him.You can also try fancy feast, clam juice or baby food.
human baby food in meat flavours (check that there are no onions or garlic in the ingredients) and mix that with warm water and offer that, or syringe it in little bits into your cat's mouth. Beech Nut makes a line of baby food that has nothing but meat (beef, chicken, turkey or veal) in it. Here's a link: http://www.beechnut.com/Our%20Baby%20Food/Results.asp If you cannot find this, you could find another meat baby food - just read the label carefully to be sure there are no onions, onion powder, garlic, or garlic powder in it.
If his tummy needs a rest, feed baby food with no onion or garlic for a few days.
If he wont eat, and your cat is not diabetic begin by giving him two droppers (cc size) of unflavored pedialyte every ten minutes for an hour. Next water down(plain water) canned cat food or baby food chicken or turkey with no onion or garlic and give only one dropper every ten minutes for another hour. Wait two hours and repeat both. When he feels hydrated he will lick up the gruel on his own.
Give him droppers of unflavored pedialyte a few times a day to make sure he stays hydrated.Called lectade in the UK and sold in the baby dept of stores.
Please let me know how he is doing. I will always be here for you.
I hope he feels better very soon.
Sincerest best wishes,