Hi..
Welcome to HEALTHCARE MAGIC..
I have gone through your query and can understand your concern..
As per your complain a painful lump on the right side of neck that is causing problem with swallowing or burning can be due to causes like infection in the submandibular 
salivary gland leading to Sialoadenosis while can also be due to obstruction in the duct of the gland caused be stone formation..
Other cause can be swollen and infected submandibular 
lymph nodes..
I would suggest you to consult an Oral Surgeon or an ENT and get evaluated and a thorough clinical evaluation and 
MRI scan will help in confirming the diagnosis and can be treated accordingly..
In case of infection antibiotics and anti-inflammatory painkiller can help..
As of now take anti-inflammatory painkiller like 
Ibuprofen and do cool compresses over the swelling..
Take a 
soft diet..
Hope this information helps..
Thanks and regards..
Dr.Honey Nandwani Arora..