I don't know if you are in the US, but if you are there are two laws that offer some protection. The first is the Family Medical Leave Act (FMLA) which alllows employees in many cases up to 12 weeks unpaid leave in a year if needed for a serious health condition. The leave can be taken in small increments, like an hour, as you needed. The employer must accomodate the leave if it applies and is looking at serious trouble if they don't. Contact U.S. Department of Labor or lawyer for more info.

The second law is Americans with Disabilities Act (ADA) which requires that employers work with employees with covered disabilities (if requested by the employee) to see if there is a way to arrange things so that they can perform the essential functions of the job with a reasonable accomodation. Time off of a limited and scheduled duration may be reasonable under the Act. Contact the Equal Employment Opportunity Commission for more detail. There are also State counterparts to these laws that sometimes offer even better protection.

Frankly, if in the US and you have been working for your employer for at least a year, have worked at least 1250 hours in a year for the employer, and the place you work isn't real small, I am guessing that the FMLA is likely to give you the right to the leave you need. But check this carefully with the Feds and/or a lawyer. And I can't tell you employers who must honor the leave law will not sometimes try to find workarounds to the anti-retaliation provisions. The good employers have folks who make sure there is no retaliation, but there are %$#@#&* everywhere.