Does two non-necrotic lymph nodes in the right axillary indicates cancer?
The axilla is outside the scope of practice for ENT.
If I'm reading your question correctly, I believe you mean the right axilla. There are numerous reasons which can cause enlarged lymph nodes. Given that your problem seems to be located axilla, also known as the armpit, I would recommend evaluation and consultation by a general surgeon or a breast surgeon.
The determination of cancer can only be made based on tissue biopsy diagnosis.
If present for two years without change, cancer is unlikely. Probably inflammatory. Get an Rx for Clindamycin or Augmentin. Apply hot, moist compresses. If it persists, a needle biopsy may be indicated.