I'm not a doctor, but my diagnosis was very similar to yours--single nodule, Hurthle cells shown on FNA biopsy, but they weren't able to tell me for sure it was cancer until I had it taken out and they looked at the entire nodule. I had the second half of my thyroid removed a month later, had radioactive iodine treatment, and have been cancer-free for three years. I was 24 years old. All my blood tests were totally normal, too.
You said you have a nodule but no lump? Isn't the nodule the lump?
It is up to you and your doctor whether it is necessary to have surgery now or if you can wait the two or three months. If it is slow-growing, that may not be enough time to see if it gets bigger. If the doctor sees that you may be at higher risk, two or three months may be too long to wait.
Also, please don't confuse RAI treatment with "radiation" that they give for other cancers. They are very very different. The RAI is a single pill that targets any remaining thyroid cells in your body. An external beam will not work. Yes, you have to stay away from other people (and animals) for two to four days to avoid damaging their thyroids (not because you will give them radiation poisoning), but after that, you're fine. No hair loss. Yes, you may get nauseated for a few hours if you are prone to it, but it passes after that. Any pain in your salivary glands can be prevented by sucking on sour candy. People have been given this treatment for thyroid cancer for more than 50 years and the long-term side-effects are very low, especially compared to the risk of not having it done at all. I went through it and compared to what other cancer patients have to go through with radiation and chemotherapy, this was a walk in the park. Even with the low-iodine diet.
You and your doctor will have to decide if the Thyrogen injections are an acceptable alternative to going off your thyroid medication. They mainly use the injection for scans, not for ablation. If you can't use them this time, you can use the injections for follow-up testing.
Only your doctor can tell you if a second biopsy would be a waste of time, but personally, I think it probably would be. No matter what it said, it wouldn't really change things because of the rates of false-negative and false-positive results. If they don't find Hurtle cells next time, that doesn't mean they weren't there, it probably means that they missed them the second time.
Call your doctor and see if you can wait for surgery until after your vacation or even a couple of months, if you really want. I don't think waiting is going to change the outcome for the better, especially beyond two or three months. If you want to get a second opinion just for your own piece of mind, do that, but it probably will be the same. Don't go see another doctor just to delay things. Do it because you really think you need to hear it from someone else.
I hope some of this cleared things up, especially about the RAI. Please feel free to write back if you have more questions or just want to discuss things. I wish you all the best.