No but it wouldn't hurt!
Seriously though, many people who have underactive thyroids have a lack of B12 in their diet, especially vegetarians. ( I should know!)
Have you had any blood tests to know that you have an underactive thyroid?
No, B12 shots have nothing to do with thyroid issues; however, you should get both thyroid and B12 levels tested. Many people who have thyroid problems are deficient in B12.