If you have hypothyroidism does that mean you will test positive for hashimotos as well?

Often, not always: Hashimoto's thyroiditis is the most common cause of hypothyroidism; most who are hypothyroid have thyroiditis- some experts say over 90%. But it does not always show up on blood tests; some with negative blood tests have positive biopsies but I don't advise biopsies. It is wise to test, as thyroiditis should be treated differently. See https://thyroidpharmacist.com/about-hashimotos/