This may or may not be appropriate. The fact that you provided a doctor's note is immaterial. Outside of FMLA, a doctor's note has no force in law. Nor does the fact that the paid sick time is available.
The only thing that matters is whether or not the time was protected under the law.
To determine that, please answer the following questions:
1.) What was the nature of the illness or illnesses? Was it the same illness in all cases?
2.) How much time did you miss on each separate occasion? One day? Three days? A week?
3.) Over what time period did these three absences occur? Were they close together? Far apart? Days apart? Weeks? Months?
4.) How many employees does your employer have within a 75 mile period?
5.) In the 12 months immediately preceding your first absence, did you work at least 1,250 hours?