I have been taking the iodine for over 3 weeks now but at different doses and with breaks. I dropped back down to 31 mcg for a few days when I was having trouble, but I am now back to 62 mcg. Is it okay to start on the selenium now or should I wait until I have been taking a consistent amount or higher amount for longer?

Since you are probably very deficient, I would just wait and not take the selenium just yet. Some people need to go very slowly. Throwing in another mineral may cause confusion and make it difficult to know what is causing what. So I would just continue taking the iodine for now until you are more comfortable with that. Slowly try to get up to a higher dosage. Then once youare taking a higher dosage of the iodine, and taking it more consistently with less trouble, then you can add in the sodium selenate.