Is Increased Dosage Of 125mg Synthroid For .41 Thyroid Number The Right Dosage?

I am on synthroid for an under active thyroid for 20 plus years. Recently my blood test required my doctor to increase my dosage from 100mcg to 125mcg. My numbers were in the 8 area. I ve been on increased dose since End of October, retested blood work Dec 6th, number was .41 tsh. Doctor said dosage was good & stay on that, but I ve had a ton of hair lose and anxiety like symptoms since middle of November. Does this sound like correct dosage for these numbers?