No.  A Form 1099 is provided to various persons to alert the IRS to payments that are likely to be taxable income to the recipient.  A person who has received a gift for personal needs as you describe has not received “income” and the donor does not need to report the payment to the IRS.

There are two specific sections of the Internal Revenue Code that may be applicable here.  Section 139 excludes from income “qualified disaster relief payments” made to pay or reimburse reasonable and necessary personal, family, or living expenses incurred as a result of a federally identified disaster, such as a major hurricane or COVID-19.  Section 102 excludes the value of property acquired by gift (other than from the recipient’s employer), without regard to how it is used or whether it is to pay expenses from a designated disaster.  A gift from one individual to another may trigger a gift tax for the donor, or a reduction in the donor’s lifetime exemption for gifts, if it exceeds $15,000 this year, but the gift is not taxable to the recipient.  Charities frequently make gifts to provide goods or services to individuals, like the payment of fees you describe or charity care at a hospital, as part of their charitable programs.  The charity is not responsible for any gift tax and the recipient is not responsible for any income tax.