Papillary thyroid cancer usually only spreads to the lymph nodes if it spreads at all and that makes little or no difference to the prognosis. Survival is still pretty close to 100% (like 99.something%), still no need for chemo or anything like that.
Odds of spread any further is about 1%-4%, I think and given your age and how small it is, I'd say your odds are lower again.
And even if it had, survival rates would still be at least 77% (I think again, they'd be significantly higher at your age, but it's hard to get stats as it's not very common).
I know you always think of the worst case scenario. I did too and in my case, the cancer was so much larger than the norm that I was thinking "well, yeah, spread is very unlikely, but a tumour of 6.7cm was pretty unlikely too and that happened."
They have to check. But the odds are very much against spread.