Hello and thanks for researching this very important question!
Green Iguanas can develop a number of conditions related to poor nutrition and infective agents. Possible causes for this swelling include:
1) Metabolic Bone Disease--a condition resulting from too-little calcium in the diet--this is the most commonly seen illness in captive reptiles. An injection of calcitonin (a special hormone) is needed to begin the healing.
2) Infection (abscess) of the tissues surrounding the jaw--strong antibiotics specific to reptiles are needed, sometimes surgical intervention is used to remove the infection
3) Tumors can invade the tissues of the face--surgical treatment is necessary
***Both of these problems do require medical assistance at this stage, since he is having trouble eating. You can make adjustments to his temperature (raise the "hot spot" to 95F degrees to help his immune system, but he should be examined.***
You can use these links to look for more nearby assistance:
http://www.reptilecare.com/herpvets.htm
http://www.herpvetconnection.com/
http://www.anapsid.org/vets/
Your concern has touched me--if you have follow-up questions, or need to clarify your case, please let me know right away! Your "Accept" helps me reach out to others!