Hello, I Have Been Diagnosed With Hypothyroidism 6 Years Ago,

Hello, I have been diagnosed with hypothyroidism 6 years ago, been on Synthroid exclusively ever since. My doctor never tested free t3 or free t4, only TSH. Recently I insisted on having free t3 and free t4 tested, because I have been unable to lose weight for the last 6 years. My levels were as followed TSH 1.12 (reference range 0.27-4.20), free t4 19 (12-22), free t3 3.6 (3.5-5.9). Upon seeing that my free t3 was low, my doctor decided to increase my dose of synthroid to 0.088 mg per day. I expected him to give me something that would treat my low t3, because I suspect that my body is not converting t4 into t3. Should I ask for a second opinion or did my doctor do the right thing by increasing my Synthroid ?? Thank you in advance.