Hmmm, that's a good question...
With candida condition they highly recommend to juice vegetables, greener the better ( :) ), go easy on carrots and beets as those are too sweet, also occasional fruit is fine, the ones are in season and not too sweet (no mango, grapes, pineapple etc.)
I hope someone who is familiar with your thyroid condition can help you - I have no idea which veggies you should avoid...
I hope you'll get better soon. :)