Hashimoto's is an autoimmune disease which can take years to develop. It is not brought on by having an IUD.
Keep your IUD.
Hashimoto's thyroiditis is stated to be a combinations of genetics with a "trigger". I haven't actually come across IUD as a trigger however childbirth can be a hormonal trigger for Hashimoto's. There may be no symptoms in the early stages of Hashimoto's. Selenium is shown to help lower TPO antibodies in various clinical trials.
Vitamin D deficiency is extremely common with Hashimoto's thyroiditis. Researchers from the University of Copenhagen have found that vitamin D is crucial to the immune system. T-cells start out inactive, but once triggered they become killer cells that seek out and destroy viruses and bacteria. T-cells will lie dormant unless they can find vitamin D. To add, vitamin D levels are lowest during winter. Optimal vitamin D levels are 50 - 80ng/mL or 125 - 200nmol/L year round.