You don't overlook a oncologist's recommendations. Eczema can cause problems like this though it is rare, and the immunizations just may have been the "trigger" that brings this problem to light. If this is the case, the immunization may have brought the problem to your attention, long before it would spread to other lymph nodes. That is a godsend to you.
Hopefully, there is no issue of cancer. But you HAVE to have the biopsy done. Take the bull by the horns and schedule it. That's the way to get over the nervous wreck part. And when this is resolved, find a specialist to help with the eczema. Don't continue using the same doctor for it that you have up until now.
Saying prayers for your little guy - and for you too!
Sending you strength.