You are not eligible to make HSA contributions if you have any "other medical coverage". This includes Medicare, so if you enrolled in medicare on May 1, that stopped your ability to contribute to an HSA, even if you were still enrolled in an HDHP. You can continue to spend the money in the account, but you can't contribute new money. If you made HSA contributions, you may have contributed too much, in which case you must withdraw the excess or pay a penalty.
Incidentally, if your daughter is "covered" by your HDHP, and is not your tax dependent, she can contribute to an HSA in her own name because she is "covered" even though she is not the policy owner. This situation will typically occur when a child is too old to be a tax dependent (age 19 or older and not a full time student, or age 24 or older, and earning more than $4400 in the year) but under age 26 and covered by a parent's insurance. So it's a limited window, but if your child is in that window, she can have her own HSA.
