First of all, take a breath.
Papillary thyroid cancer has a very very high cure rate--80 to 90% for ALL cases. Also, your nodule is less than 1 cm, giving you even better odds. It being that small also means that it is unlikely to have spread beyond the thyroid, for one thing. Thyroid cancers also tend to be slow growing. It might get a little bigger (probably still staying under 1 cm in that amount of time), but it's not going to spread that quickly. Your doctor should have gone over all of this with you, but you can also look it up online. There is a ton of information about Papillary Thyroid cancer (just be sure to only look at the Papillary stuff, because the other types don't apply to you and no, they don't mistake one for the other once they've diagnosed it).
Has the doctor talked to you about Radioactive Iodine Treatment after your surgery? It's possible that he thinks it may not be necessary since your nodule is so small, but if you do have it, then what that does is remove ALL thyroid cells in your body that may not have been removed by the surgery, in case any cancer did spread (still unlikely). At early stages, it's usually used to make follow-up blood tests and scans more accurate. Then you'll have follow-up scans and blood tests, basically every 6 months to a year for the rest of your life to make sure everything is okay.
I went through all of this 6 years ago when I was 24. Been cancer-free ever since. I know that it's very scary. The waiting is *AWFUL*, I know. It seems like you're either waiting on an ultrasound or a biopsy or the surgery. But you are on the right track.
If you want to find another surgeon, you could try (just don't cancel the first appointment), but I think it's more important to have a surgeon that you trust, who has experience and will do a good job. If you aren't comfortable with the one you have, then by all means, keep looking.
Just please stop stressing yourself so much. You're not dying. Don't let this rule your life. Go out an enjoy things. Screw cancer! Don't let that little bump keep you from your life. Now go call a friend and go out and have a steak or whatever you want and celebrate life. Go do what makes you happy. Even if you don't feel like doing it, you might find yourself enjoying it despite yourself.
If you have more questions or just want to vent, please feel free to re-post. Best of luck to you.