Diagnosed w/Hashimoto's 20 years ago, had a TT 2 years ago. My TSH levels jumping from the very low range to being too high. What might cause this?

Under active thyroid. Has humorous can start with an over active thyroid but ultimately it damages the thyroid gland. A high TSH means your Thyroid gland is not producing enough thyroid hormone and your body is "kicking it" to make it work harder. If the level is very high you will probably need thyroid hormone pills.