Since you know you feel depressed when you are hypothyroid, and since you can't know if you are without the thyroid tests, I think it makes sense to start there. I suspect that once you are back on your thyroid meds regularly your depression lessen and your bbt will normalize. Another symptom of hypothyroidism, besides depression, is feeling cold and I don't know but I would assume then the bbt is affected.
My thyroid med through Walmart is $4 a month and less for a 3-month supply.