This could be swollen lymph gland, abscessed tooth or possibly an salivary gland problem depending on where on the neck it is. Usually with a salivary gland problem you will also see excessive drooling.
Swollen lymph nodes can be due to many causes including infections, autoimmune diseases, fungal and bacterial infections and lymphoma (cancer). You can read about the lymphatic system in the dog here:
An abscessed tooth can sometimes cause lumps or swelling of the muzzle or jaw and upper neck. You will want to check your dog’s mouth and look for any broken or discolored teeth. If you find any, buffered aspirin can be given to a dog with a dosage of up to 5 mg per pound every 12 hours for pain until your dog can be seen by your Vet. Keep in mind that a dog's body does not metabolize aspirin in the same way as a human and thus should not be given more than a day or two without contacting your Vet.
Check just under your dog’s jawbone for a swelling and under your dog’s tongue for a swelling. This is where some of your dog’s salivary glands are located. If you find a swelling here, it’s possible your dog has an accumulation of fluid near the salivary gland called a sialocele which is causing your dog to salivate more. This condition does require your dog to be seen as soon as possible. You can read about it here:
You will need to have your dog seen so the cause is identified and treated. Since finances might be an issue, you may want to see if the following organization can help.
Care Credit http://www.carecredit.com
Quick application and approval for care credit card. You can sometimes apply and get approval while you are at the vet office.
This group helps low income families with vet care.
This organization help people with emergency medical care in some cases.
American Animal Hospital Association
Helps animals that have been abandoned or if the owner is having financial hardships
Angels 4 Animals http://www.Angels4Animals.org
This organization offers financial aid or treatment to those pets and owners in need.
God's Creatures Ministry
Help pay Vet bills for those that need help
The Pet Fund http://thepetfund.com/
Helps provide emergency vet care to those in need.
United Animal Nations http://www.uan.org/lifeline/index.html
They help rescuers, low income and homeless pay for vet care.
I hope this information helps.