No, the reasons listed for the new sick and the family leave credits are all Covid related. The same rules apply to the self-employed. Here is a link for reference.
The are no other family leave credits available for self-employed taxpayers.
The Family Leave credit is for periods of leave during which they are unable to work or telework due to a need for leave to care for a child of such employee if the child’s school or place of care has been closed (including the closure of a summer camp, summer enrichment program, or other summer program), or because the child care provider of the child is unavailable, for reasons related to COVID-19.
The sick leave credit is for:
An employee who is unable to work (including telework) because of coronavirus quarantine or self-quarantine or has coronavirus symptoms and is seeking a medical diagnosis.
An employee who is unable to work due to caring for someone with coronavirus, or caring for a child because the child’s school or place of care is closed, or the paid child care provider is unavailable due to the coronavirus.