Yes you can deduct the interest on your construction loan if the loan was secured by the property you moved into.
You can treat a home under construction as a qualified home for a period of up to 24 months, but only if it becomes your qualified home at the time it is ready for occupancy. The 24-month period can start any time on or after the date that construction begins.
See page 4 under Qualified Home and Home Under Construction: https://www.irs.gov/pub/irs-pdf/p936.pdf
Yes, you can treat a construction loan as a deductible home mortgage, as long as you complete construction within 24 months and convert the construction loan to a regular mortgage when the home is finished. However, if you do not complete construction and move into the home within 24 months from the start of construction, the loan does not become a deductible mortgage and you would have to go back and amend your tax returns to remove the deduction.