I have hypothyroidism, hashimotos. My recent bloodwork shows I have low iron, high uibc and tibc and heavy periods. What could be the cause?

Heavy periods. Hashimoto is an autoimmune inflammatory process in thyroid gland. It is separate problem to the low iron. If you have low ferritin and high tibc- that means you have iron deficiency. This iron deficiency is likely due to /related to your heavy period. You should take some iron replacement. Heavy periods can be related to your hypothyroidism. See you md and d/w your md more detail.
Iron deficiency. You are iron deficient from your heavy periods. Hashimoto's with hypothyroidism, if under treated, can contribute to heavy periods.