Do I have a claim?

Unless you had PTO (i.e. sick days/vacation time or coverage under the FMLA (Family Medical Leave Act) or ADA (Americans with Disablites Act), you had no right to be out of work. Attendance is a basic job requirement, so it was perfectly permissable to terminate you due to your absences. In fact, unless you had protection under an employment contract or union agreement, as an "at will" worker you could have been fired for any reason or no reason at all. 

Unfortunately, they are right: your health is your concern, not your employer's--if you missed work without having sick days or other paid time off which you had earned or accrued to cover the absence, it was an unauthorized absence, which you could be terminated for. The law does not guaranty or give you the right to miss work, even for health reason, unless you use PTO or were able to use (e.g. you were eligible for, your employer covered by, your condition justified, *and* you informed your employer you were using) Family and Medical Leave Act (FMLA) leave. Indeed, if you did not have a written employment contract guarantying or protecting your employment, you were an "employee at will" and could be terminated at any time, for any reason--employees at will have essentially no rights in or to their employment. Based on what you write, you appear to have no recourse.