Side effects are unlikely because of the low dose and the short time you will take the drug.
Possible side effects include skin rashes, swelling of the salivary glands, and "iodism" (metallic taste, burning mouth and throat, sore teeth and gums, symptoms of a head cold and sometimes stomach upset and diarrhea. A few people have an allergic reaction with more serious symptoms. Those could be fever and joint pain, or swelling of parts of the face and body and at times severe shortness of breath requiring immediate medical attention.
Taking iodide may rarely cause over activity, under activity or enlargement of the thyroid gland (goiter.)
If the side effects are severe of if you have an allergic reaction, stop taking potassium iodide and call a doctor or public health authority for instructions.