Your state tax obligations are based on your state of domicile. Your domicile is your main, permanent home. Massachusetts' rule on changing domicile is that "each person keeps his or her own present domicile until he or she establishes a new domicile in another place." https://www.mass.gov/service-details/learn-about-legal-and-residency-status-in-massachusetts
Since your time in Florida was temporary and transitory, you did not establish a new domicile there.
Therefore, you remained residents of MA for tax purposes until the day you began living in your new NH home, which became your new domicile on that day. All your income prior to that date is taxable by MA.
So for 2019 you'll file a part-year resident MA tax return, and in TT you'll enter your NH move-in date as the date your residency changed.
NH does not have an income tax, but it does tax interest and dividends above certain threshold amounts. You can read the details here: https://www.revenue.nh.gov/faq/interest-dividend.htm
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
