Endos treat your hormones, ENT's are surgeons who treat the neck area. I tend to favor the ENT's over the Endo, because I had a lobectomy, they found cancer, and all three surgeons said to remove the other side, the Endo said it was not necessary. I listened to the surgeons, and they found the big tumor during the second surgery. 9mm's is just under the threshold for doing a biopsy, they like it to be 1 cm, but you can request a biopsy. I had a complex nodule on one side, and three solid nodules on the other, they did not test the complex nodule, that is where the biggest cancerous tumor was found. Even after the first surgery, the Endo did an ultrasound and did not recommend that we take it out. Glad I listened to the ENT's. My sister had one nodule about 9 mm, the doc did do a biopsy and found cancer. I would request a biopsy if you can get one.
I would suggest that you go to a "thyroid" specialist which would be a Endocrinologist. Although ENT's do specialize in Thyroid as well, i believe that Endocrinogolist's are well aware of thyroid issues. The most important thing about a nodule is not size but what's in it. If there are abnormal cells, shrinking the nodule will not eliminate the issue.
I was sent to a Physician for a nodual that was 11mm not an endo,( As i had thyroid problems i went on meds that shrunk it to 4mm, so far so good) but we dont have one where i am, a lot here do go to endos for thyroid problems, do you have any other issues with your thyroid? Have they been able to biopsy it? What did a scan show? I dont think 9mm is big some are a lot bigger, Some times they dont biopsy till they are 1cm they will just keep a watch, mine will be checked each 6 months..