Have a read of this article and consider natural thyroid stimulation such as dissicated thyroid re: t3 and t4, as well kelp and/or other iodine sea vegetables, ashwagandha works on the thyroid AND adrenals (the other reason) and possibly Colostrum for the thymus gland - this is touted to balance auto-immune related symptoms such as allergies - autoimmune hypothyroidism. The adrenals and/or an imbalance of estrogen and testosterone would be related to yeasty condition.
Taking ALL sugars out of the diet is best - which would mean going with raw or home cooked - this means no grains, potato's, pea's, legumes, fruit, carrots anything carbohydrate.
Also, titer instead of re-vaccinating - related to auto-immune disfunction...see the links inside of the article above and read this on colostrum
COLOSTRUM FOR DOG ALLERGIES Dogs Naturally Magazine
BOVINE COLOSTRUM: THE FORGOTTEN MIRACLE Dogs Naturally Magazine
Also note, if using synthetic hormone replacement - essentially the thyroid is going to stop working altogether - by stimulting with the right food, natural thyroid replacement and herbs, it can start to work and produce on it's own...5-6 yrs. is young - this is more an 8 yr. + malfunction - so I would think it is autoimmune related