I was told by a tax professional that if I was without health insurance for a total of 3 months, 2 of those months are allowed at no penalty. How do I apply this?

Sorry, that is not right.

If you were without insurance for 2 months or less, there would be no penalty.  If you were without insurance for 3 or more months (however, if you had insurance for at least 1 day in a month, that counts as an insured month), the penalty applies to all months, unless you qualify for an exemption.

https://www.healthcare.gov/health-coverage-exemptions/exemptions-from-the-fee/