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I am not expert in US labor law, but the guidance given by the Department of Labor with regard to the federal Fair Labor Standards Act (FLSA), at http://www.dol.gov/compliance/guide/minwage.htm, is as follows:

The Act does not limit either the number of hours in a day or the number of days in a week that an employer may require an employee to work, as long as the employee is at least 16 years old. Similarly, the Act does not limit the number of hours of overtime that may be scheduled. However, the Act requires employers to pay covered employees not less than one and one‑half times their regular rates of pay for all hours worked in excess of 40 in a workweek, unless the employees are otherwise exempt.

This assumes, of course, that the employment is not exempt from the provisions of the FLSA. A workweek is a period of 168 hours and may start on any day of the week. Further information is available at http://www.dol.gov/esa/whd/ and http://www.dol.gov/elaws/faq/esa/flsa/toc.htm.

The FLSA does not set any rules with regard to sickness payments. My reading of this suggests that the extra hours worked in the second week cannot be treated as offsetting the hours missed in the first week, and that the extra 8 hours in the second week should therefore be treated as overtime.

I have also looked at Texas labor law provisions at http://www.twc.state.tx.us/customers/bemp/bempsub5.html, but there does not appear to be anything relevant there.

There may, however, be factors that I am not aware of, and I hope someone with more experience of US labor law will also comment on this question.