If eyebrows fell because of high TSH level, what should I do: take thyroid medication or take eyebrow regrowth treatment?

If you believe you lost eyebrow hair due to a thyroid condition, you should treat the thyroid condition. You need to see a doctor for a proper exam and treatment options.

Hypothyroidism is known to cause thinning of the eyebrows, particularly in the lateral 1/3.  Since you have an elevated TSH, you may have hypothyroidism and you should be followed.  I agree that since the level is not that abnormal (and assuming your other thyroid function test are normal) that watchful waiting is a good decision.  So continue to follow with your doctor, hold any medication, and follow your thyroid function tests over time.  (Typically about every 6 weeks).  If they are abnormal again, you need a full work up.  Until you are sure your thyroid is not contributing to your eyebrow hair loss you should not consider other treatments for your eyebrows.

Be sure to see a hair specialist for advice. Your eyebrow loss may not be directly related to your thyroid fluctuations, but your hair specialist can advise you. If your eyebrow loss is related to thyroid abnormalities, then yes, the TSH must come into the normal range. Options such as minoxidil or bimatoprost can be discussed with your physician. Eyebrow density does not always improve even when the thyroid levels are normalized. 

You need to see a doctor and get a diagnosis. For me to guess without you in front of me and all of your lab tests, would be wrong. A good dermatologist is the best person to see. 

What you are describing sounds like alopecia areata of the eyelashes caused by thyroid imbalance.  If thyroid function is the only systemic abnormality,  the eyelashes will not regrow until the underlying thyroid imbalance is corrected.  At that point,  if the eyelashes don't regrow on their own,  your dermatologist can help with therapy.