I am sorry to hear you are worried about Tigger. I am a veterinarian and will do my best to help.
How large is the lump? 2 inches? More, or less? Does it hurt him when you touch it?
A lump in this area could be an enlarged lymph node, an abscess (infected pocket of pus), or a growth of some sort. If he were my own dog, I would do an FNA (fine needle aspirate) on it by gently inserting a needle to get some fluid or cells from the lump, to examine microscopically and try to find out what it is. Since he is not eating, I am concerned it could be painful, or an infection.
How much amoxicillin are you giving him, and how much does he weigh? If this is an abscess, it may need to be lanced, flushed, and drained; antibiotics alone may not be enough. If the infection is trapped inside an abscess, the antibiotics in his blood stream do not reach it.
Warm compresses may help if this is an abscess, but it would be best to have it checked by your veterinarian. Some baby aspirin may help if it is painful, but I do not recommend giving aspirin to a dog that is not eating. I need his weight to give you a safe and effective dose of things like amoxicillin and aspirin.
Let me know how he is doing and if I can help with or answer anything else. Rebecca