Yes, you may. If your significant other had no legal obligation to pay your medical expenses, they can be considered a gift to you, which will allow you to deduct the expenses in the year paid.
See http://www.ustaxcourt.gov/InOpHistoric/La5ng.TCM.WPD.pdf A key point in the case was “petitioner [Judith Lang] was not a minor, and Mrs. Field [Judith Lang’s mother] was not legally obligated to pay petitioner’s expenses.” If Mrs. Field was obligated to pay the expenses, then her daughter may not have been able to deduct them, as they wouldn’t have been a gift.
To enter medical expenses, click on Where do I enter my medical expenses?