Edit: Sorry, just saw this was in Ask the Nurses. Not a nurse, but gave a reply based on my experience of thyroid cancer. Sorry, replied without looking at the forum.

Papillary thyroid cancer is very slow-growing. It is unlikely a couple of months would make any difference whatsoever.

Whether they do any follow-up treatment or not will depend on how much of a risk they deem you to be at for reccurrence. They might do radioiodine treatment, which would mean basically that you swallow a capsule to remove any remaining thyroid tissue. It's kind of annoying because you have to go on a low iodine diet for two weeks beforehand and then, you have to restrict your movements a bit for a couple of weeks afterwards as you are radioactive, but it's not painful or likely to make you sick or anything. And there isn't any great rush with it as a general rule.

It's very likely you are now cancer-free, but they will be able to tell you more on the 19th and confirm if you will need any more treatment. Even if you do, the main job is done. 

Papillary thyroid cancer is a pretty mild form of cancer for most people. If you are under about 50, the survival rate is over 99%, I think and even for older people, the survival rate is really high.

Thank you for getting back to me so quickly and for the info. It's reassuring and it has calmed me, although I still can't help being anxious, the joys of having severe anxiety.

Thank you again.