Hello and welcome - It is very common for TSH to remain suppressed early in the treatment process. Hopefully, your doctor is basing your dosing on Free T4 and T3 and NOT on TSH alone!
Most patients who have high blood pressure in association with hyperthyroidism will start to see some relief as levels approach the normal range. However, hopefully, your doc is keeping an eye on this and will work with you if it gets to the point where treatment might be recommended.
Take care - and keep us posted!
GDATF Forum Facilitator
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