Sounds more like a serious side effect of Benicar than worsening hyperthyroid symptoms. There is a listed interaction for thyroid function tests but states "without associated thyroid disturbance."
Excerpts from the Drug website...
"Benicar HCT (hydrochlorothiazide / olmesartan) Disease Interactions...
"Thiazides (Includes Benicar HCT) ↔ Thyroid Function Tests
Moderate Potential Hazard, Moderate plausibility
Applies to: Thyroid Disease
Thiazide diuretics may decrease serum PBI (protein-bound iodine) levels without associated thyroid disturbance. Clinicians should be cognizant of this effect when prescribing or administering thiazide therapy to patients with thyroid disorders."
Benicar side effects
"Get emergency medical help if you have any of these signs of an allergic reaction to Benicar: hives; difficulty breathing; swelling of your face, lips, tongue, or throat.
Call your doctor at once if you have:
a light-headed feeling, like you might pass out;
little or no urinating;
severe or ongoing diarrhea with weight loss;
chest pain, fast heart rate; or
swelling in your hands or feet.
Common Benicar side effects may include:
This is not a complete list of side effects and others may occur."