thyroid cancer only affect thyroid function in fewer cases. most times people have it and have no thyroid malfunction at all.
i would still get it checked, i had thyroid cancer four years ago and the process to get it removed isn't as bad as you might scare yourself to be. If you are to get it removed, make sure the surgeon is a specialist- you don't want to end up with a raspy voice or a big incision.
gluten intolerance/celiac is most definitely related to papillary thyroid cancer. wishing you the best and hopefully it's just your lymph nodes fighting off a minor infection