I am T1, but I had the same test done that you did. Don't worry about protecting other people from the radiation - it's a low enough dose that you yourself are not harmed at all by it, so everyone else around you will be just fine too. It's not like your urine or breath will be radioactive. Well, your urine might be a teeny tiny bit, but not enough that they will hold you on-site for it. Some radiation tests/treatments do require that you stay in a special area with special facilites b/c your urine is too radioactive for normal systems.
I was working in a lab at the time of my test, I was also the radiation safety officer for the lab, so believe me, I asked all about the dose, the amount, where it would go, how it would decay, whether I would be radioactive, whether I would contaminate anything or anyone, etc! After I swallowed the pill, I went back to work, and the whole afternoon I used the geiger counter on myself (that machine that beeps a lot when it finds radiation)... I went around the lab putting it on my stomach and my throat (cause eventually that's where it all ended up) and freaked everybody out! It was fun.
I do hope you get good test results, but if it turns out you have an overactive thyroid, it's very easily treatable. My hyperthyroidism (Graves' Disease) went away after treating it for 1-2 years! Good luck!